During the week of October 23-27,1989, Northwestern University hosted an international conference on the theme "Diffusion Processes and Related Problems in Analysis." This was attended by 105 partici­ pants representing 14 different countries. The conference, which is part of the "Emphasis Year" program traditionally supported by the Mathematics Department, was additionally supported by grants from the National Science Foundation, the National Security Agency, the Institute for Mathematics and Applications, as well as by supplemen­ tary sources from Northwestern University. The purpose of this meeting was to bring together workers in various parts of probability theory, mathematical physics, and partial dif­ ferential equations. Previous efforts in this direction were represented by the 1987 AMS Summer Research Conference "Geometry of Random Motion" co-sponsored with Rick Durrett, the proceedings of which ap­ peared as volume 73 in the AMS series "Contemporary Mathematics." The present effort is intended to extend beyond the strictly geometric theme and to include problems of large deviations, shastic flows, and other areas of shastic analysis in which diffusion processes play a leading role.