This volume consists of 24 papers submitted for publicationby the invited speakers of the IFIP International Conferenceon Stochastic Partial Differential Equations and their Ap-plications. Most of them are research papers, however, a fewsurveys written by world renowed experts are also included.The aim of the conference was to bring together mathematici-ans, physicists and engineers representing academic as wellas industrial fields, interested in the theory and applica-tions of SPDE's. The field of SPDE's is one of the most dy-namically developing areas at the cross roads of severalsciences. It is especially attractive for many because ofits interdisciplinary character and enormous richness ofal-ready existing as well as potential applications. There wereabout one hundred participants registered for the conferen-ce. With rare exceptions, all of the most active researchersin the field of SPDE's throughout the world were present atthe conference. The main topics for discussion at the confe-rence were: non-linear SPDE's and Markov property for randomfields, modern stochastic calculuses, numerical and asympto-tic methods for SPDE's, applications of SPDE's with emphasisonnon-linear filtering, stochastic control and statisticalfluid dynamics.