At the intersection of physics, mathematics, and computer science, an exciting new field of study has formed, known as “Topological Quantum.” This research field examines the deep connections between the theory of knots, special types of subatomic particles known as anyons, certain phases of matter, and quantum computation. This book elucidates this nexus, drawing in topics ranging from quantum gravity to topology to experimental condensed matter physics. Topological quantum has increasingly been a focus point in the fields of condensed matter physics and quantum information over the last few decades, and the forefront of research now builds on the basic ideas presented in this book. The material is presented in a down-to-earth and entertaining way that is far less abstract than most of what is in the literature. While introducing the crucial concepts and placing them in context, the subject is presented without resort to the highly mathematical category theory that underlies the field. Requiring only an elementary background in quantum mechanics, this book is appropriate for all readers, from advanced undergraduates to the professional practitioner. This book will be of interest to mathematicians and computer scientists as well as physicists working on a wide range of topics. Those interested in working in these field will find this book to be an invaluable introduction as well as a crucial reference.

Extremely timely, well structured and engaging, exposing both the mathematical beauty of the subject and its deep connections to physics. * Kirill Shtengel, University of California, Riverside *
This text is nothing short of a triumph. * Kymani Armstrong-Williams, Physics Book Reviews *
I recommend the book to everyone who is interested in topological quantum field theories, topological quantum computing and topological materials. I also recommend it to students to get an impression of current hot topics. * Torsten Asselmeyer-Maluga, MathSciNet *

Steven H. Simon is a theoretical physics professor at Oxford University and a professorial fellow of Somerville College, Oxford. Before coming to Oxford he was director of theoretical physics research at Bell Laboratories. He has served on the UK EPSRC Physical Sciences Strategic Advisory Board. He is known for his work on Topological Phases of Matter, Topological Quantum Computation, and Fractional Quantum Hall Effect. He is the author of a popular introductory book on solid state physics, entitled The Oxford Solid State Basics which has been used at over a hundred universities worldwide.