This book consolidates and brings up to date the variational theory and methods currently used in many branches of theoretical physics and chemistry. The text surveys essential ideas and methods, concentrating on theory as used in applications rather than on fine points of rigorous mathematics. Essential concepts are developed in a common notation and from a uniform critical point of view. The theory underlying practical computational methods is developed. Examples of important applications are reviewed in sufficient detail to provide the reader with a critical understanding of context and methodology.