Academic Press, 1979. 308 pages. In the summer of 1977 I was invited to lecture in the Troisieme Cycle de la Suisse Romande, a consortium of four universities in the French-speaking part of Switzerland. There was some discussion of the topic about which I might speak. Since I seem fated to be the apostle of probability to Swiss physics (see ), we agreed on the general topic of "path integral techniques." I decided to limit myself to the well-defined Wiener integral rather than the often ill-defined Feynman integral. In preparing my lectures I was struck by the mathematical beauty of the material, especially some of the ideas about which I had previously been unfamiliar. I was also struck by the dearth of "expository" literature on the connection between Wiener integral techniques and their application to rather detailed ques- tions in differential equations, especially those of quantum physics; it seemed that path integrals were an extremely powerful tool used as a kind of secret weapon by a small group of mathematical physicists. My pur- pose here is to rectify this situation. I hope not only to have made available new tools to practicing mathematical physicists but also to have opened up new areas of research to probabilists. I am pleased to be able to thank some of my colleagues who aided me in the preparation of this book. During the period of the lectures on which the book is based, I was a guest of the Physics Department of the University of Geneva. I am grateful to M. Guenin, the departmental chairman, and most especially to J. P. Eckmann for making my visit possible. The lectures were given at the EPFL in Lausanne; P. Choquard was a most gracious host there. I should like to thank the Secretariat Centrale of the University of Geneva Physics Department and Mrs. G. Anderson of the Princeton Physics Department for typing the first and second drafts, respectively, of the manuscript. I am also grateful to Y. Kannai for the hospitality of the Weizmann Institute Pure Mathematics Department where Sections 20-24 were written. Finally, I owe a debt to a number of people for scientific contributions: M. Donsker and M. Kac made various valuable suggestions about what topics might be included as well as offering help on technical questions; L. van Hemmen gave his permission to use an unpublished argument of his; I had valuable discussions with M. Aizenman, R. Carmona, P. Deift, J. P. Eckmann, J. Frohlich, C. Gruber, E. Lieb, A. Sokal, M. Taylor, A. Truman, and S. R. S. Varadhan; the careful reading of the complete manu- script by R. Carmona was especially valuable; finally, M. Klaus, A. Kupiainen, and K. Miller helped in the proofreading. I am glad to be able to thank all these individuals for their help.
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