"This is a very interesting book on an important topic both for physics and for mathematics. (...) It starts at the beginning, but is not really for beginners; the physics background develops rapidly, through seven short chapters, and the final eight chapters provide a lightning review of the mathematical topics encountered (...) Part II is the main part of the text, containing a selection of fascinating topics, beautifully presented, to many of which the author has been a significant contributor. The chapters on functional integration, on elliptic operators, their determinants and related index theorems, on calculating instanton contributions and on anomalies are particularly attractive. (...)"Bulletin London Mathematical Society
0 Background.- 1 Fundamental Concepts.- 2 The Degree of a Map.- 3 The Fundamental Group and Covering Spaces.- 4 Manifolds.- 5 Differential Forms and Homology in Euclidean Space.- 6 Homology and Cohomology.- 7 Homotopy Classification of Maps of the Sphere.- 8 Homotopy Groups.- 9 Fibered Spaces.- 10 Fibrations and Homotopy Groups.- 11 Homotopy Theory of Fibrations.- 12 Lie Groups.- 13 Lie Algebras.- 14 Topology of Lie Groups and Homogeneous Manifolds.- 15 Geometry of Gauge Fields.- Index of Notation.