Nine survey articles in this volume extend concepts from classical probability and stochastic processes to a number of areas of mathematical physics. Key topics covered: nonlinear stochastic wave equations, completely positive maps, Mehler-type semigroups on Hilbert spaces, entropic projections, martingale problem and Markov uniqueness of infinite- dimensional Nelson diffusions, analysis in geometric probability theory, measure-preserving shifts on the Wiener space, cohomology on loop spaces, and stochastic Volterra equations Contributors: H. Airault * L. Coutin * L. Decreusefond * C. Leonard * R. Leandre * P. Lescot * P. Malliavin * M. Oberguggenberger * R. Rebolledo * F. Russo * A.S. Ustunel * L. Wu The work, an outgrowth of a workshop on stochastic analysis held in Lisbon, serves as a good reference text for researchers and advanced students in the fields of probability, stochastic processes, analysis, geometry, math physics, and physics.