The 2nd edition of LNM 523 is based on the two first authors' mathematical approach of this theory presented in its 1st edition in 1976. An entire new chapter on the current forefront of research has been added. Except for this new chapter and the correction of a few misprints, the basic material and presentation of the first edition has been maintained. At the end of each chapter the reader will also find notes with further bibliographical information.

Presents an overview of the mathematical realization of Feynman path integrals in terms of well-defined functional integrals, that is, the infinite dimensional oscillatory integrals. This book contains the traditional results on the topic.

Sergio Albeverio gave important contributions to many fields ranging from Physics to Mathematics, while creating new research areas from their interplay. Some of them are presented in this Volume that grew out of theRandom Transformations and Invariance in Stochastic DynamicsWorkshop held in Verona in 2019. To understand the theory of thermo- and fluid-dynamics, statistical mechanics, quantum mechanics and quantum field theory, Albeverio and his collaborators developed stochastic theories having strong interplays with operator theory and functional analysis. His contribution to the theory of...