This volume contains the Proceedings of the five-day Third Seminar on Stochastic Analysis, Random Fields and Applications, which took place at the Centro Stefano Franscini (Monte Verita) in Ascona (Ticino), Switzerland, from Monday, Septem­ ber 20 to Friday, September 24, 1999. The first two editions of this conference oc­ cured in 1993 and 1996. The Seminar focused on three topics: fundamental aspects of stochastic analysis, physical modeling, and applications to financial engineering. As in 1993 and 1996, the third topic was the subject of the Third Minisymposium on Stochastic Methods in Financial Models. A major topic within Stochastic Analysis is the area of stochastic partial differen­ tial equations. The state of the art of a large part of this subject was presented in several lectures, that covered equations driven by correlated Gaussian noise in high space dimension, the relationship with super-Brownian motion and popu­ lation dynamics, Malliavin calculus and asymptotics of law densities, stochastic algorithms and control theory. While of fundamental nature, several of these sto­ chastic equations have also recently been used in the study of interest rates in finance. In Physical Modeling, recent developments in quantum field theory, kinetic the­ ory and magnetic fields were presented. This area was explored more extensively than in the two previous editions during a special session on TUesday afternoon dedicated, on the occasion of his sixtieth birthday, to Professor Sergio Albeverio.