Covering recent developments in the field, this updated text provides an introduction to the ideas and techniques of differential geometry and topology. In this edition, the applications have been greatly expanded and additional problems have been included. The author examines anomalies in gauge field theories, bosonic string theory, Brane-World cosmology, Seiberg-Witten invariants, and topological quantum computing. A solutions manual is available for qualifying instructors.

Praise for Previous Editions:?a very impressive book.-Australian and New Zealand Physicist The clarity of the presentation is enhanced by explicit calculations and diagrams ? There is also a large number of exercises and problems, and last but not least, an index ? superb layout?-Zentralblatt fur Mathematick