Roderich Moessner is director at the Max Planck Institute for the Physics of Complex Systems in Dresden. His theoretical discoveries include classical and quantum spin liquids, emergent magnetic monopoles, and non-equilibrium spatiotemporal ordering phenomena. He is recipient of the Leibniz Prize and of the Europhysics Prize, Honorary Fellow of Hertford College, Oxford, and member of the Executive Board of the German Physical Society. Joel E. Moore is Chern-Simons Professor of Physics at the University of California, Berkeley and Senior Faculty Scientist at Lawrence Berkeley National Laboratory. His research interests include topological insulators, semimetals, and semiconductors, along with the application of quantum information concepts to many-body physics. He is a Simons Investigator, a Fellow and former elected Member-at-Large of the American Physical Society, and Chair of the Advisory Board of the Kavli Institute for Theoretical Physics.

'… a timely and valuable introduction to the most important theoretical concepts in the topological study of matter … brief treatment of a vast, rapidly evolving subject that currently dominates condensed matter physics … This book is appropriate for physics collections within all university libraries.' M. C. Ogilvie, Choice Connect

• Preface; Acknowledgements; 1. Introduction; 2. Basic concepts of topology and condensed matter; 3. Integer topological phases; 4. Geometry and topology of wavefunctions in crystals; 5. Hydrogen atoms for fractionalisation; 6. Gauge and topological field theories; 7. Topology in gapless matter; 8. Disorder and defects in topological phases; 9. Topological quantum computation via non-Abelian statistics; 10. Topology out of equilibrium; 11. Symmetry, topology, and information; Appendix; References; Index.