Stochastic ordering is a fundamental guide for decision making under uncertainty. It is also an essential tool in the study of structural properties of complex stochastic systems. This reference text presents a comprehensive coverage of the various notions of stochastic orderings, their closure properties, and their applications. Some of these orderings are routinely used in many applications in economics, finance, insurance, management science, operations research, statistics, and various other fields of study. And the value of the other notions of stochastic orderings still needs to be explored further. This book is an ideal reference for anyone interested in decision making under uncertainty and interested in the analysis of complex stochastic systems. It is suitable as a text for advanced graduate course on stochastic ordering and applications. Moshe Shaked is Professor of Mathematics at the University of Arizona, Tucson, AZ. He has made several fundamental contributions to the development of stochastic ordering and stochastic convexity, with applications in reliability theory and economics. He has published over 150 papers in this and related areas. J. George Shanthikumar is Professor of Industrial Engineering and Operations Research at the University of California, Berkeley, CA. He has made fundamental contributions to the application of stochastic ordering and stochastic convexity to queueing and related problems that arise in operations research and management science. He has published over 250 papers in this and related fields.