This text serves as a pedagogical introduction to the theoretical
concepts on application of topology in condensed matter systems. It
covers an introduction to basic concepts of topology, emphasizes
the relation of geometric concepts such as the Berry phase to
topology, having in mind applications in condensed matter. In
addition to describing two basic systems such as topological
insulators and topological superconductors, it also reviews
topological spin systems and photonic systems. It also describes
the use of quantum information concepts in the context of
topological phases and phase transitions, and the effect of
non-equilibrium perturbations on topological systems.This book
provides a comprehensive introduction to topological insulators,
topological superconductors and topological semimetals. It includes
all the mathematical background required for the subject. There are
very few books with such a coverage in the market.
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