Topics in Spatial Stochastic Processes : Lectures given at the C.I.M.E. Summer School held in Martina Franca Italy July 1 8 2001 The theory of stochastic processes indexed by a partially ordered set has been the subject of much research over the past twenty years. The objective of this CIME International Summer School was to bring to a large audience of young probabilists the general theory of spatial processes including the theory of set indexed martingales and to present the different branches of applications of this theory including stochastic geometry spatial statistics empirical processes spatial estimators and survival analysis. This theory has a broad variety of applications in environmental sciences social sciences structure of material and image analysis. In this volume the reader will find different approaches which foster the development of tools to modelling the spatial aspects of stochastic problems