This book contains lecture notes by world experts on one of the most rapidly growing fields of research in physics. Topological quantum phenomena are being uncovered at unprecedented rates in novel material systems. The consequences are far reaching, from the possibility of carrying currents and performing computations without dissipation of energy, to the possibility of realizing platforms for topological quantum computation.The pedagogical lectures contained in this book are an excellent introduction to this blooming field. The lecture notes are intended for graduate students or advanced undergraduate students in physics and mathematics who want to immerse in this exciting XXI century physics topic.

This Les Houches Summer School presents an overview of this field, along with a sense of its origins and its placement on the map of fundamental physics advancements. The School comprised a set of basic lectures (part 1) aimed at a pedagogical introduction of the fundamental concepts, which was accompanied by more advanced lectures (part 2) covering individual topics at the forefront of today's research in condensed-matter physics.

About the Author:
Claudio Chamon, Professor of Physics, Physics Department, Boston University, USA, Mark O. Goerbig, CNRS Research Director, Laboratoire de Physique des Solides, CNRS UMR, Universite Paris-Sud, France, Roderich Moessner, Director, Max-Planck-Institute fur Physik komplexer Systeme, Germany, Leticia F. Cugliandolo, Professor, Sorbonne Universites, Universite Pierre et Marie Curie, Laboratoire de Physique Theorique et Hautes Energues, CNRS UMR, France

Claudio Chamon is Professor of Physics at Boston University. He studied at MIT, where he received his BS degree in Aeronautics & Astronautics (1989), MS in Electrical Engineering and Computer Science (1991), and PhD in Physics (1996). He was a postdoctoral fellow at the Univ. of Illinois at Urbana Champaign (1996-1998) and a member at the Institute for Advanced Study (1999). His research focuses on topological states of matter and on systems out-of-equilibrium. He is Fellow of the American Physical Society.

Mark Oliver Goerbig obtained a joint PhD degree from the Universities of Fribourg (Switzerland) and Paris-Sud (France) in 2004 on correlated electronic phases in quantum Hall systems. After a year of postdoctoral research on frustrated quantum magnetism at the University Pierre et Marie Curie, Paris, he was awarded a CNRS researcher position at Laboratoire de Physique des Solides, Orsay, where he started to work on graphene and related topological materials, in addition to his ongoing research on the quantum Hall effect. Since 2012, he is also professor at the Ecole Polytechnique in Palaiseau.

Professor Roderich Moessner is Director at the Max Planck Institute for the Physics of Complex Systems. He has previously held faculty positions at Ecole Normale Superieure in Paris as well as at Oxford University, where he had also done his doctoral studies, which were followed by a postdoctoral appointment at Princeton University. His research interests are in theoretical condensed matter and statistical physics as well as quantum information theory. In particular, he investigates the physics of strong fluctuations in many-body systems, which may be due to frustration, competing degrees of freedom or quantum fluctuations. Among the prizes he has received are the Europhysics Prize of the Condensed Matter Division of the European Physical Society and the Leibniz Prize of the German Science Foundation.

Leticia F. Cugliandolo received her Ph.D. in theoretical physics from the Universidad Nacional de La Plata, Argentina, in 1991. After post-docs in Universita di Roma I, La Sapienza, and CEA/Saclay she joined the Physics Department at Ecole Normale Superieure de Paris in 1997. She is currently a full professor at Universite Pierre et Marie Curie in Paris and the director of Ecole de Physique des Houches since 2007. Her research focuses on statistical physics and condensed matter problems. She received the Marie Curie Excellence Award, the Guggenheim Fellowship and the Prix Langevin of the French Physical Society.