Concepts drawn from topology and differential geometry have become essential to the understanding of several phenomena in condensed matter physics. This book provides a self-consistent introduction to the mathematical ideas and methods from these fields that will enable the student of condensed matter physics to begin applying these concepts with confidence. This expanded second edition adds eight new chapters, including one on the classification of topological states of topological insulators and superconductors and another on Weyl semimetals, as well as elaborated discussions of the Aharonov-Casher effect, topological magnon insulators, topological superconductors and K-theory.

Key Features:

• Provides an introduction to path integral formalism

• Introduces all the basic concepts in differential geometry and topology

• Presents the quantum Hall effect using topology concepts

• Includes an introduction to topological insulators

• Presents the Weyl semimetal using topological concepts

• Studies spin systems using topology