This volume, divided into seven sections, reflects the wide range of Peter Whittle's professional interests and his search for underlying unity. It includes papers on quantum probability, polymers, communication theory, epidemics, queues, large deviations, nonlinear systems, neural networks, spatial statistics, sequential analysis, optimization, Gittins indices and Markov decision processes. Fascinating linkages are made between these normally disparate subject areas. Students in applicable mathematics whether in statistics, probability or optimization will find this essential reading. Peter Whittle's career has spanned over forty years, during which he has produced eight major volumes and numerous papers. He has often emphasized the coherence of the broad area of applicable mathematics and the context it provides for the disciplines of statistics and operational research.