This book is devoted to the study and optimization of spatiotemporal stochastic processes, that is, processes which develop simultaneously in space and time under random influences. These processes are seen to occur almost everywhere when studying the global behavior of complex systems, including • physical and technical systems, • population dynamics, • neural networks, • computer and telecommunication networks, • complex production networks, • flexible manufacturing systems, • logistic networks and transportation systems, • environmental engineering, • climate modelling and prediction, • earth surface models. Classical stochastic dynamic optimization forms the framework of the book. Taken as a whole, the project undertaken in the book is to establish optimality or near-optimality for Markovian policies in the control of spatiotemporal Markovian processes. The authors apply this general principle to different frameworks of Markovian systems and processes. Depending on the structure of the systems and the surroundings of the model classes the authors arrive at different levels of simplicity for the policy classes which encompass optimal or nearly optimal policies. A set of examples accompanies the theoretical findings, and these examples should demonstrate some important application areas for the theorems discussed. Audience This book is intended for experts in applied mathematics, cybernetics, and in the theory of optimal control.