Collected together in this book are ten expository articles on the most important topics in optimization, written by leading experts in the field. The book provides a primary reference for those performing research in some area of optimization or for those who have an elementary basic knowledge of optimization techniques but wish to learn the most up-to-date and efficient algorithms for particular classes of problems. The first sections of each chapter are expository and therefore accessible to master's level graduate students. However, the chapters also contain advanced material on current topics of interest to researchers. For instance, there are chapters which describe the polynomial-time linear programming algorithms of Khachian and Karmarkar and the techniques used to solve combinatorial and integer programming problems, an order of magnitude larger than was possible just a few years ago. The work contains a coherent view of the important unifying ideas throughout the many facets of optimization and a guide to the most significant current areas of research.