The field of global optimization has been developing at a rapid pace. There is a journal devoted to the topic, as well as many publications and notable books discussing various aspects of global optimization. This book is intended to complement these other publications with a focus on shastic methods for global optimization. Shastic methods, such as simulated annealing and genetic algorithms, are gaining in popularity among practitioners and engineers be­ they are relatively easy to program on a computer and may be cause applied to a broad class of global optimization problems. However, the theoretical performance of these shastic methods is not well under­ stood. In this book, an attempt is made to describe the theoretical properties of several shastic adaptive search methods. Such a theoretical understanding may allow us to better predict algorithm performance and ultimately design new and improved algorithms. This book consolidates a collection of papers on the analysis and development of shastic adaptive search. The first chapter introduces random search algorithms. Chapters 2-5 describe the theoretical analysis of a progression of algorithms. A main result is that the expected number of iterations for pure adaptive search is linear in dimension for a class of Lipschitz global optimization problems. Chapter 6 discusses algorithms, based on the Hit-and-Run sampling method, that have been developed to approximate the ideal performance of pure random search. The final chapter discusses several applications in engineering that use shastic adaptive search methods.