Now in paperback, this book provides a self-contained introduction to the cohomology theory of Lie groups and algebras and to some of its applications in physics. No previous knowledge of the mathematical theory is assumed beyond some notions of Cartan calculus and differential geometry (which are nevertheless reviewed in the book in detail). The examples, of current interest, are intended to clarify certain mathematical aspects and to show their usefulness in physical problems. The topics treated include the differential geometry of Lie groups, fibre bundles and connections, characteristic classes, index theorems, monopoles, instantons, extensions of Lie groups and algebras, some applications in supersymmetry, Chevalley-Eilenberg approach to Lie algebra cohomology, symplectic cohomology, jet-bundle approach to variational principles in mechanics, Wess-Zumino-Witten terms, infinite Lie algebras, the cohomological descent in mechanics and in gauge theories and anomalies. This book will be of interest to graduate students and researchers in theoretical physics and applied mathematics.

‘[This book] reserves for itself a special place among other presentations by successfully trying to be self-contained. Its strong point is a systematic exposition of the mathematical background in an accessible form … the book is most useful for physicists who want to go beyond the standard physics review type introduction to differential geometry. The book offers them a quite rigorous but at the same time lucid and self-contained presentation.’

Source: Mathematical Reviews

‘This book is a useful contribution to the constantly growing literature that is devoted to the mathematics-physics interface …The book is a welcome relief to the physicist searching for a physically motivated yet mathematically rigorous and systematic exposition of gauge anomalies … The book under review reserves itself a special place among other presentations by successfully trying to be self-contained. Its strong point is a systematic exposition of the mathematical background in an accessible form … a quite rigorous but at the same time lucid and self-contained presentation.’

Source: Mathematical Reviews

‘The material presented is essentially self-contained and at a basic graduate text level. The material is also well organized and the book reads very well … The book is warmly recommended.’

Source: Classical and Quantum Gravity