Acquaints graduate students with basic ideas and methods of modern differential geometry and their applications in physics. Half of the chapters focus on local analysis, useful for graduate students of theoretical physics. Three chapters discuss geometry of fiber bundles, and the last four chapters deal with the Atiyah-Singer index theorem, its generalization and its application, quantum anomaly, cohomology field theory, and noncommutative geometry. Eighteen appendices offer background in topology and algebra. Annotation c. by Book News, Inc., Portland, Or.