Assuming a familiarity with quantum field theory and relativity, Nakahara (physics, Kinki University) explains the basic concepts of algebraic topology and differential geometry, defines the various types of fiber bundles and connections on fiber bundles, and applies the methods to anomalies appearing in gauge theories. The second edition adds the proof of the index theorem in terms of supersymmetric quantum mechanics. Distributed in the U.S. by AIDC.