Title from publisher's bibliographic system (viewed on 05 Oct 2015).

The physical and mathematical environment -- An inheritance from physics -- A toolkit from analysis -- Feynman's integral versus Kac's integral -- Quantum mechanics -- First lesson : gaussian integrals -- Semiclassical expansion : WKB -- Semiclassical expension : beyond WKB -- Quantum dynamics : path integrals and the operator formalism -- Methods from differential geometry -- Symmetries -- Homotopy -- Grassmann analysis : basics -- Grassmann analysis : applications -- Volume elements, divergences, gradients -- Non-gaussian applications -- Poisson processes in physics -- A mathematical theory of Poisson processes -- The first exit time : energy problems -- Problems in quantum field theory -- Renormalization 1 : an introduction -- Renormalization 2 : scaling -- Renormalization 3 : combinatorics / contributed by Markus Berg -- Volume elements in quantum field theory / contributed by Bryce DeWitt -- Projects -- Appendix A : Forward and backward integrals, spaces of pointed paths -- Appendix B : Product integrals -- Appendix C : A compedium of gaussian integrals -- Appendix D : Wick calculus / contributed by Alexander Wurm -- Appendix E : The Jacobi operator -- Appendix F : Change of variables of integration -- Appendix G : Analytic properties of covariances -- Appendix H : Feynman's checkerboard.

Functional integration successfully entered physics as path integrals in the 1942 Ph.D. dissertation of Richard P. Feynman, but it made no sense at all as a mathematical definition. Cartier and DeWitt-Morette have created, in this book, a fresh approach to functional integration. The book is self-contained: mathematical ideas are introduced, developed, generalised and applied. In the authors' hands, functional integration is shown to be a robust, user-friendly and multi-purpose tool that can be applied to a great variety of situations, for example: systems of indistinguishable particles; Aharonov-Bohm systems; supersymmetry; non-gaussian integrals. Problems in quantum field theory are also considered. In the final part the authors outline topics that can be profitably pursued using material already presented.