Equivariant Cohomology and the Localization Principle -- Finite-Dimensional Localization Theory for Dynamical Systems -- Quantum Localization Theory for Phase Space Path Integrals -- Equivariant Localization on Simply Connected Phase Spaces: Applications to Quantum Mechanics, Group Theory and Spin Systems -- Equivariant Localization on Multiply Connected Phase Spaces: Applications to Homology and Modular Representations -- Beyond the Semi-Classical Approximation -- Equivariant Localization in Cohomological Field Theory -- Appendix A: BRST Quantization -- Appendix B: Other Models of Equivariant Cohomology.

This book, addressing both researchers and graduate students, reviews equivariant localization techniques for the evaluation of Feynman path integrals. The author gives the relevant mathematical background in some detail, showing at the same time how localization ideas are related to classical integrability. The text explores the symmetries inherent in localizable models for assessing the applicability of localization formulae. Various applications from physics and mathematics are presented.