The instant New York Times bestsellerQuanta and Fields, the second book of Sean Carroll’s already internationally acclaimed series The Biggest Ideas in the Universe, is an adventure into the bare stuff of reality.   Sean Carroll is creating a profoundly new approach to sharing physics with a broad audience, one that goes beyond analogies to show how physicists really think. He cuts to the bare mathematical essence of our most profound theories, explaining every step in a uniquely accessible way.   Quantum field theory is how modern physics describes nature at its most profound level. Starting with the basics of quantum mechanics itself, Sean Carroll explains measurement and entanglement before explaining how the world is really made of fields. You will finally understand why matter is solid, why there is antimatter, where the sizes of atoms come from, and why the predictions of quantum field theory are so spectacularly successful. Fundamental ideas like spin, symmetry, Feynman diagrams, and the Higgs mechanism are explained for real, not just through amusing stories. Beyond Newton, beyond Einstein, and all the intuitive notions that have guided homo sapiens for millennia, this book is a journey to a once unimaginable truth about what our universe is. Read more

Would you like to know how the universe works? Scientists have been asking that question for a long time and have found that many of the answers can be found in the study of particle physics, the field that focuses on those impossibly tiny particles with unbelievably strange names - the hadrons and leptons, baryons and mesons, muons and gluons - so mystifying to the rest of us. And now, in a fascinating and accessible series of 24 lectures, you can take the mystery out of the remarkable field that in only 100 years has unlocked the secrets of the basic forces of nature. Professor Pollock will make you familiar with the fundamental particles that make up all matter, from the tiniest microbe to the sun and stars. And you'll also learn the "rules of the game" - the forces that drive those particles and the ways in which they interact - that underlie the workings of the universe. The lectures have been designed to be enriching for everyone, regardless of scientific background or mathematical ability. Virtually all you'll need as you enter this fascinating world are your curiosity, common sense, and, as Professor Pollock notes, "an open mind for the occasional quantum weirdness." As you move through the lectures, you'll also gain a knowledge of how those particles fit into perhaps the greatest scientific theory of all time: the Standard Model of particle physics; a grasp of key terms like "gauge symmetry," "quantum chromodynamics," and "unified quantum field Theory;" and an appreciation of how particle physics fits in with other branches of physics - including cosmology and quantum mechanics - to create our overall understanding of nature. Read more

Feynman’s bestselling introduction to the mind-blowing physics of QED—presented with humor, not mathematicsCelebrated for his brilliantly quirky insights into the physical world, Nobel laureate Richard Feynman also possessed an extraordinary talent for explaining difficult concepts to the public. In this extraordinary book, Feynman provides a lively and accessible introduction to QED, or quantum electrodynamics, an area of quantum field theory that describes the interactions of light with charged particles. Using everyday language, spatial concepts, visualizations, and his renowned Feynman diagrams instead of advanced mathematics, Feynman clearly and humorously communicates the substance and spirit of QED to the nonscientist.With an incisive introduction by A. Zee that places Feynman’s contribution to QED in historical context and highlights Feynman’s uniquely appealing and illuminating style, this Princeton Science Library edition of QED makes Feynman’s legendary talks on quantum electrodynamics available to a new generation of readers. Read more

Anyone who truly wants to understand general relativity, quantum field theory or any other area of modern physics first needs to master Lagrangian mechanics.The issue with most resources teaching Lagrangian mechanics is that they don't truly teach you the why behind it. But what if it didn't have to be that way? What if you could truly learn Lagrangian mechanics the right way?The truth is that trying to understand physics at a deep level without understanding Lagrangian mechanics is like driving a car without a steering wheel – you’ll eventually run into a wall and not be able to move forward anymore.The issue is that Lagrangian mechanics is often taught in a way that does not truly explain why it's needed and instead leaves you wondering “who cares about this?”The true reason why Lagrangian mechanics is so incredibly powerful is that it gives you a general framework for describing literally any area of modern physics.This is the reason why Lagrangian mechanics exists, but almost no one will teach you it this way... even though they should.Whether you want to learn:ElectrodynamicsSpecial and general relativityQuantum field theoryString theoryYou absolutely need to have a deep understanding of Lagrangian mechanics to even get started on any of these topics.However, getting started and specifically knowing where to start is often the most difficult part. It would be nice to have a dedicated resource that introduces Lagrangian mechanics completely from scratch and gives you everything in one place.Well, that's exactly what this book will give you.You'll learn Lagrangian mechanics in a completely unique way you've likely never seen before - as both a fundamental framework for advanced modern physics, but also as an incredibly powerful problem solving tool.Lagrangian Mechanics For The Non-Physicist is a complete resource specifically designed to teach you everything you'd possibly need to know about Lagrangian mechanics and the foundations of modern physics - the fundamentals, prerequisites, theory, math and practical applications. It's all here.Some of the interesting you'll be able to learn from this book include:The intuition and proper motivation for why Lagrangian mechanics works and how it's useful in the first place as well as why the principle of stationary action makes senseCalculus of variations - the area of math Lagrangian mechanics uses - from the ground up, starting from the very basic ideas of single-variable calculusThe framework of Lagrangian mechanics, how to set up and solve any Lagrangian mechanics problem in a consistent step-by-step fashionA deeper dive into topics like generalized coordinates, generalized momenta, Lagrange multipliers and solving problems with constraintsAdvanced topics not covered in most other books - the most notable ones including friction and non-conservative forces in Lagrangian mechanics, solving statics problems with the principle of virtual work as well as a bottom-up approach to d'Alembert's principleThe relation between symmetries and conservation laws, described by Noether's theorem, as well as a precise description of what we even mean by symmetries in physicsSome advanced applications to modern physics, such as relativistic energy conservation and conservation of probability in quantum mechanics Read more

Quanta and Fields, the second book of Sean Carroll’s already internationally acclaimed series The Biggest Ideas in the Universe, is an adventure into the bare stuff of reality.   Sean Carroll is creating a profoundly new approach to sharing physics with a broad audience, one that goes beyond analogies to show how physicists really think. He cuts to the bare mathematical essence of our most profound theories, explaining every step in a uniquely accessible way.   Quantum field theory is how modern physics describes nature at its most profound level. Starting with the basics of quantum mechanics itself, Sean Carroll explains measurement and entanglement before explaining how the world is really made of fields. You will finally understand why matter is solid, why there is antimatter, where the sizes of atoms come from, and why the predictions of quantum field theory are so spectacularly successful. Fundamental ideas like spin, symmetry, Feynman diagrams, and the Higgs mechanism are explained for real, not just through amusing stories. Beyond Newton, beyond Einstein, and all the intuitive notions that have guided homo sapiens for millennia, this book is a journey to a once unimaginable truth about what our universe is. Read more

A celebration of the seemingly simple idea that allowed us to imagine the world in new dimensions—sparking both controversy and discovery.  The stars of this book, vectors and tensors, are unlikely celebrities. If you ever took a physics course, the word “vector” might remind you of the mathematics needed to determine forces on an amusement park ride, a turbine, or a projectile. You might also remember that a vector is a quantity that has magnitude and (this is the key) direction. In fact, vectors are examples of tensors, which can represent even more data. It sounds simple enough—and yet, as award-winning science writer Robyn Arianrhod shows in this riveting story, the idea of a single symbol expressing more than one thing at once was millennia in the making. And without that idea, we wouldn’t have such a deep understanding of our world.Vector and tensor calculus offers an elegant language for expressing the way things behave in space and time, and Arianrhod shows how this enabled physicists and mathematicians to think in a brand-new way. These include James Clerk Maxwell when he ushered in the wireless electromagnetic age; Einstein when he predicted the curving of space-time and the existence of gravitational waves; Paul Dirac, when he created quantum field theory; and Emmy Noether, when she connected mathematical symmetry and the conservation of energy. For it turned out that it’s not just physical quantities and dimensions that vectors and tensors can represent, but other dimensions and other kinds of information, too. This is why physicists and mathematicians can speak of four-dimensional space-time and other higher-dimensional “spaces,” and why you’re likely relying on vectors or tensors whenever you use digital applications such as search engines, GPS, or your mobile phone.In exploring the evolution of vectors and tensors—and introducing the fascinating people who gave them to us—Arianrhod takes readers on an extraordinary, five-thousand-year journey through the human imagination. She shows the genius required to reimagine the world—and how a clever mathematical construct can dramatically change discovery’s direction. Read more

Providing a comprehensive introduction to quantum field theory, this textbook covers the development of particle physics from its foundations to the discovery of the Higgs boson. Its combination of clear physical explanations, with direct connections to experimental data, and mathematical rigor make the subject accessible to students with a wide variety of backgrounds and interests. Assuming only an undergraduate-level understanding of quantum mechanics, the book steadily develops the Standard Model and state-of-the art calculation techniques. It includes multiple derivations of many important results, with modern methods such as effective field theory and the renormalization group playing a prominent role. Numerous worked examples and end-of-chapter problems enable students to reproduce classic results and to master quantum field theory as it is used today. Based on a course taught by the author over many years, this book is ideal for an introductory to advanced quantum field theory sequence or for independent study. Read more

Quantum field theory is arguably the most far-reaching and beautiful physical theory ever constructed, with aspects more stringently tested and verified to greater precision than any other theory in physics. Unfortunately, the subject has gained a notorious reputation for difficulty, with forbidding looking mathematics and a peculiar diagrammatic language described in an array of unforgiving, weighty textbooks aimed firmly at aspiring professionals. However, quantum field theory is too important, too beautiful, and too engaging to be restricted to the professionals. This book on quantum field theory is designed to be different. It is written by experimental physicists and aims to provide the interested amateur with a bridge from undergraduate physics to quantum field theory. The imagined reader is a gifted amateur, possessing a curious and adaptable mind, looking to be told an entertaining and intellectually stimulating story, but who will not feel patronised if a few mathematical niceties are spelled out in detail. Using numerous worked examples, diagrams, and careful physically motivated explanations, this book will smooth the path towards understanding the radically different and revolutionary view of the physical world that quantum field theory provides, and which all physicists should have the opportunity to experience.To request a copy of the Solutions Manual, visit http://global.oup.com/uk/academic/physics/admin/solutions. Read more

Feynman’s bestselling introduction to the mind-blowing physics of QED—presented with humor, not mathematicsCelebrated for his brilliantly quirky insights into the physical world, Nobel laureate Richard Feynman also possessed an extraordinary talent for explaining difficult concepts to the public. In this extraordinary book, Feynman provides a lively and accessible introduction to QED, or quantum electrodynamics, an area of quantum field theory that describes the interactions of light with charged particles. Using everyday language, spatial concepts, visualizations, and his renowned Feynman diagrams instead of advanced mathematics, Feynman clearly and humorously communicates the substance and spirit of QED to the nonscientist.With an incisive introduction by A. Zee that places Feynman’s contribution to QED in historical context and highlights Feynman’s uniquely appealing and illuminating style, this Princeton Science Library edition of QED makes Feynman’s legendary talks on quantum electrodynamics available to a new generation of readers. Read more

Quantum field theory is arguably the most far-reaching and beautiful physical theory ever constructed, with aspects more stringently tested and verified to greater precision than any other theory in physics. Unfortunately, the subject has gained a notorious reputation for difficulty, with forbidding looking mathematics and a peculiar diagrammatic language described in an array of unforgiving, weighty textbooks aimed firmly at aspiring professionals. However, quantum field theory is too important, too beautiful, and too engaging to be restricted to the professionals. This book on quantum field theory is designed to be different. It is written by experimental physicists and aims to provide the interested amateur with a bridge from undergraduate physics to quantum field theory. The imagined reader is a gifted amateur, possessing a curious and adaptable mind, looking to be told an entertaining and intellectually stimulating story, but who will not feel patronised if a few mathematical niceties are spelled out in detail. Using numerous worked examples, diagrams, and careful physically motivated explanations, this book will smooth the path towards understanding the radically different and revolutionary view of the physical world that quantum field theory provides, and which all physicists should have the opportunity to experience. Read more

This second edition of Particles in the Dark Universe has been substantially enhanced with several new chapters that delve into crucial aspects of particle physics in the Universe. These additions encompass the role of primordial black holes in the early universe, tracing their formation to decay, unification theories, a comprehensive historical overview of cosmological models, an extensive examination of the physics of the graviton, and an educational exploration of gravitational phenomena such as Unruh-type or Hawking radiation. Additionally, this edition incorporates 30 new exercises and provides a comprehensive presentation of inflationary models, along with a pedagogical insight into the mechanism of baryogenesis.Structured in a logical sequence, this book offers a thorough and instructional exploration of particle physics within the early universe. It initiates by elucidating the thermal history of the universe, delving into pivotal concepts like Big Bang nucleosynthesis, the cosmic microwave background (CMB), and inflation. Subsequently, it meticulously addresses both direct and indirect detection methods of dark matter, followed by an in-depth analysis of neutrino physics. The book further scrutinizes potential candidates for dark matter and their interactions.Designed for theoretical physicists engaged in particle physics within the universe, dark matter detection, astrophysical constraints, and those interested in models of inflation or reheating, this book also caters to astrophysicists involved in quantum field theory computations. It encompasses all essential elements required for computing various physical processes, providing mathematical tables, necessary thermodynamic functions for the early universe, and Feynman rules. Consequently, this book serves as an intersecting point between astrophysics, particle physics, and cosmology. Read more

Quantum field theory is the basis of our modern description of physical phenomena at the fundamental level. This systematic and comprehensive text emphasizes nonperturbative phenomena and supersymmetry. It includes a thorough discussion of various phases of gauge theories, extended objects and their quantization, and global supersymmetry from a modern perspective. This Second Edition is revised to include topics developed in the last decade, including higher-form global symmetries and their applications, anomalies in supersymmetric theories beyond Ferrara–Zumino, and non-Abelian supersymmetric vortex strings. A new final part is added, presenting more than 90 problems with detailed solutions, allowing students to check their understanding of the acquired knowledge and providing extra details to supplement the main text descriptions. This an indispensable book for graduate students and researchers in theoretical physics. Read more

An exceptionally accessible introduction to quantum field theoryQuantum field theory is by far the most spectacularly successful theory in physics, but also one of the most mystifying. This venerable subject provides the crucial bridge between the long established quantum mechanics and the still hypothetical string theory. Quantum Field Theory, as Simply as Possible provides an essential primer on the subject, giving readers the conceptual foundations they need to wrap their heads around one of the most important yet baffling subjects in physics.Quantum field theory grew out of quantum mechanics in the late 1930s and was developed by a generation of brilliant young theorists, including Julian Schwinger and Richard Feynman. Their predictions were experimentally verified to an astounding accuracy unmatched by the rest of physics. Quantum field theory unifies quantum mechanics and special relativity, thus providing the framework for understanding the quantum mysteries of the subatomic world. With his trademark blend of wit and physical insight, A. Zee guides readers from the classical notion of the field to the modern frontiers of quantum field theory, covering a host of topics along the way, including antimatter, Feynman diagrams, virtual particles, the path integral, quantum chromodynamics, electroweak unification, grand unification, and quantum gravity.A unique and valuable introduction for students and general readers alike, Quantum Field Theory, as Simply as Possible explains how quantum field theory informs our understanding of the universe, and how it can shed light on some of the deepest mysteries of physics. Read more

"A great delight to read." — Physics TodayAmong the most fertile areas of modern physics, many-body theory has produced a wealth of fundamental results in all areas of the discipline. Unfortunately the subject is notoriously difficult and, until the publication of this book, most treatments of the topic were inaccessible to the average experimenter or non-specialist theoretician.The present work, by contrast, is well within the grasp of the nonexpert. It is intended primarily as a "self-study" book that introduces one aspect of many-body theory, i.e. the method of Feynman diagrams. The book also lends itself to use as a reference in courses on solid state and nuclear physics which make some use of the many-body techniques. And, finally, it can be used as a supplementary reference in a many-body course.Chapters 1 through 6 provide an introduction to the major concepts of the field, among them Feynman diagrams, quasi-particles and vacuum amplitudes. Chapters 7 through 16 give basic coverage to topics ranging from Dyson's equation and the ladder approximation to Fermi systems at finite temperature and superconductivity. Appendixes summarize the Dirac formalism and include a rigorous derivation of the rules for diagrams. Problems are provided at the end of each chapter and solutions are given at the back of the book.For this second edition, Dr. Mattuck, formerly of the H. C. Orsted Institute and the University of Copenhagen, added to many chapters a new section showing in mathematical detail how typical many-body calculations with Feynman diagrams are carried out. In addition, new exercises were included, some of which gave the reader the opportunity to carry out simpler many-body calculations himself. new chapter on the quantum field theory of phase transitions rounds out this unusually clear, helpful and informative guide to the physics of the many-body problem. Read more

While theoretical particle physics is an extraordinarily fascinating field, the incredibly fast pace at which it moves along, combined with the huge amount of background information necessary to perform cutting edge research, poses a formidable challenge for graduate students. This book represents the first in a series designed to assist students in the process of transitioning from coursework to research in particle physics. Rather than reading literally dozens of physics and mathematics texts, trying to assimilate the countless ideas, translate notations and perspectives, and see how it all fits together to get a holistic understanding, this series provides a detailed overview of the major mathematical and physical ideas in theoretical particle physics. Ultimately the ideas will be presented in a unified, consistent, holistic picture, where each topic is built firmly on what has come before, and all topics are related in a clear and intuitive way.This introductory text on quantum field theory and particle physics provides both a self-contained and complete introduction to not only the necessary physical ideas, but also a complete introduction to the necessary mathematical tools. Assuming minimal knowledge of undergraduate physics and mathematics, this book lays both the mathematical and physical groundwork with clear, intuitive explanations and plenty of examples. The book then continues with an exposition of the Standard Model of Particle Physics, the theory that currently seems to explain the universe apart from gravity. Furthermore, this book was written as a primer for the more advanced mathematical and physical ideas to come later in this series. Read more

A brilliantly diverting and mind-expanding guide to quantum and particle physics.At the start of the twentieth century, our knowledge of science appeared complete and it seemed that the laws of nature were almost all discovered, but then we woke a sleeping giant—we discovered quantum mechanics. In the quantum realm, objects can be in two places at once. It’s a place where time travel is not only possible, but necessary. It’s a place where cause and effect can happen in reverse and observing something changes its state. From parallel universes to antimatter, quantum mechanics has revealed that when you get right down to it, the laws of nature are insane. The scientist J. B. S. Haldane once said, “Reality is not only stranger than we imagine, it’s stranger than we can imagine.” Never is this more true than with quantum mechanics. This comprehensive beginner’s guide to quantum mechanics explains not only the weirdness of the subject but the experiments that proved it to be true. Using a humorous and light-hearted approach, Fundamental tells the story of how the most brilliant minds in science grappled with seemingly impossible ideas and gave us everything from microchips to particle accelerators. Fundamental gives clear explanations of all the quantum phenomena known to modern science, without requiring an understanding of complex mathematics; it tells the eccentric stories of the scientists who made these shattering discoveries and what they used them for; it explains how quantum field theory (a topic not covered in detail by any other popular-science book) gave rise to particle physics and why the Higgs boson isn’t the end of the story. Read more

Have you ever wondered how the universe works at its most fundamental level? How space and time intertwine, why black holes exist, or what quantum mechanics reveals about reality? This book offers a clear, step-by-step guide to modern theoretical physics, presenting its most groundbreaking ideas in a way that is engaging, accessible, and free of complex equations.Written for curious minds, students, and science enthusiasts alike, this non-technical yet comprehensive introduction breaks down the deep mysteries of physics in a structured, easy-to-follow format. Whether you want to understand the laws governing motion, explore the strange world of quantum mechanics, or dive into the cosmic vastness of general relativity, this book will take you on an eye-opening journey through the pillars of modern physics.____What You’ll Discover Inside:✅ Classical Mechanics – Explore Newton’s laws, energy conservation, and the deep principles that describe motion and forces.✅ Relativity & The Nature of Space and Time – Grasp Einstein’s revolutionary ideas, from time dilation and spacetime curvature to the mind-bending implications of black holes.✅ Quantum Mechanics – Unravel the bizarre world of wave-particle duality, superposition, uncertainty, and entanglement—ideas that challenge our very understanding of reality.✅ Quantum Field Theory & The Standard Model – Discover how fundamental forces and particles interact, from quarks and leptons to the Higgs boson.✅ Cosmology & The Fate of the Universe – Understand the Big Bang, dark matter, dark energy, and the expanding cosmos.✅ The Quest for a Unified Theory – Explore groundbreaking ideas like string theory, loop quantum gravity, and the search for a "Theory of Everything."✅ The Philosophy of Physics – Reflect on the nature of reality, free will vs. determinism, and how mathematical beauty shapes scientific theories.✅ The Historical Timeline of Theoretical Physics – Follow the key discoveries that revolutionized our understanding of the universe.____Who Is This Book For?🔹 Curious Learners & Science Enthusiasts – No physics background? No problem! This book is designed to explain complex ideas in simple terms without requiring advanced mathematics.🔹 Students & Aspiring Physicists – Whether you’re a high school or college student, this book will strengthen your understanding of physics fundamentals before diving into more advanced studies.🔹 Lifelong Learners & Thinkers – If you love big ideas, deep questions, and expanding your understanding of reality, this book is a must-read.____Why This Book?✔️ Step-by-Step Approach – Each chapter builds on the last, guiding you through theoretical physics without overwhelming complexity.✔️ No Advanced Math Required – While physics is mathematical at its core, this book explains concepts intuitively, making it accessible to all readers.✔️ Comprehensive Yet Easy to Follow – Covers all the major topics in modern theoretical physics without unnecessary jargon.✔️ Engaging and Thought-Provoking – Discover the mysteries of the universe in a way that sparks curiosity and deep thinking.____Are You Ready to Explore the Universe?This book is your gateway to understanding the deepest laws of nature—from the forces that govern motion to the fundamental structure of reality itself. Whether you’re looking to build a strong foundation in physics or simply want to explore the biggest questions in science, this book will take you on an inspiring intellectual adventure. Read more

A synthesis of historical literature and emerging research suggests the modern-day quantum field theory (QFT) in physics was understood by cultures of antiquity (Shabana, 2012; Quehenberger, 2013). For example, the customs and practices of the ancient Egyptians align with the tenets of QFT, which suggest the tangible world as we know it, is entirely composed of frequency and vibration. Recognizing that all elements of temporal existence are variations of frequency and vibration has profound implications for multiple fields in modern science, including medicine.While modern science understands matter as composed of atomic and subatomic particles that constitute a molecular structure, traditional perspectives of physics are largely based upon notions of physical solids interacting with one another, rather than recognizing the non-solid nature of objects and the dynamic, mutually intertwined influence of multi-dimensional waves. Emerging discoveries support QFT and the notion that the material world, as perceived by modern humans, is composed entirely of vibrations (Shabana, 2012). Moreover, vibratory frequencies and their spectrum quality likely extend infinitely beyond the limited range of frequencies that are perceivable to the normative senses of humans. Most vibrations occur at extremely subtle levels, either above or below the perceivable range. Vibratory frequency composes matter, consciousness, sensation, perception, and reaction, underscoring the inseparable confluence of mind, body, spirit, and consciousness. These concepts were well understood by many cultures of antiquity, most notably the ancient Egyptians (Quehenberger, 2013). Literature and ancient artifacts indicate that the Egyptians possessed knowledge of the nature of the cosmos and embodied a more expansive, holistic understanding of both the nature of temporal reality as vibration and the influence of higher dimensions and consciousness on the temporal, physical world (Quehenberger, 2013). Examining these concepts in light of the modern QFT provides ontological insights that contextualize the nature of reality and existence. Read more

With the exponential growth of program trading in the global financial industry, quantum finance and its underlying technologies have become one of the hottest topics in the fintech community. Numerous financial institutions and fund houses around the world require computer professionals with a basic understanding of quantum finance to develop intelligent financial systems. This book presents a selection of the author’s past 15 years’ R&D work and practical implementation of the Quantum Finance Forecast System – which integrates quantum field theory and related AI technologies to design and develop intelligent global financial forecast and quantum trading systems. The book consists of two parts: Part I discusses the basic concepts and theories of quantum finance and related AI technologies, including quantum field theory, quantum price fields, quantum price level modelling and quantum entanglement to predict major financial events. Part II then examines the current, ongoingR&D projects on the application of quantum finance technologies in intelligent real-time financial prediction and quantum trading systems.  This book is both a textbook for undergraduate & masters level quantum finance, AI and fintech courses and a valuable resource for researchers and data scientists working in the field of quantum finance and intelligent financial systems. It is also of interest to professional traders/ quants & independent investors who would like to grasp the basic concepts and theory of quantum finance, and more importantly how to adopt this fascinating technology to implement intelligent financial forecast and quantum trading systems. For system implementation, the interactive quantum finance programming labs listed on the Quantum Finance Forecast Centre official site (QFFC.org) enable readers to learn how to use quantum finance technologies presented in the book. Read more

Manifolds, the higher-dimensional analogs of smooth curves and surfaces, are fundamental objects in modern mathematics. Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classical mechanics, general relativity, and quantum field theory. In this streamlined introduction to the subject, the theory of manifolds is presented with the aim of helping the reader achieve a rapid mastery of the essential topics. By the end of the book the reader should be able to compute, at least for simple spaces, one of the most basic topological invariants of a manifold, its de Rham cohomology. Along the way, the reader acquires the knowledge and skills necessary for further study of geometry and topology. The requisite point-set topology is included in an appendix of twenty pages; other appendices review facts from real analysis and linear algebra. Hints and solutions are provided to many of the exercises and problems. This work may be used as the text for a one-semester graduate or advanced undergraduate course, as well as by students engaged in self-study. Requiring only minimal undergraduate prerequisites, 'Introduction to Manifolds' is also an excellent foundation for Springer's GTM 82, 'Differential Forms in Algebraic Topology'. Read more