M Ideals in Banach Spaces and Banach Algebras This book provides a comprehensive exposition of M ideal theory a branch ofgeometric functional analysis which deals with certain subspaces of Banach spaces arising naturally in many contexts. Starting from the basic definitions the authors discuss a number of examples of M ideals (e.g. the closed two sided ideals of C* algebras) and develop their general theory. Besides applications to problems from a variety of areas including approximation theory harmonic analysis C* algebra theory and Banach space geometry are presented. The book is mainly intended as a reference volume for researchers working in one of these fields but it also addresses students at the graduate or postgraduate level. Each of its six chapters is accompanied by a Notes and Remarks section which explores further ramifications of the subject and gives detailed references to the literature. An extensive bibliography is included