Elements of noncommutative geometry

In recent years noncommutative geometry has been a rich topic of research with discoveries leading to an increasing number of applications in mathematics and theoretical physics. Very little has appeared in book form since Alain Connes' work in the early 90s to deal with this subject. "Elements of Noncommutative Geometry" fills an important gap in the literature. Key features of the work include: * unified and comprehensive presentation of core topics and key research results drawing from several branches of mathematics * rigorous, well-written, nearly self-contained exposition of noncommutative geometry and some of its useful applications to quantum theory * excellent exposition of introductory material; main topics covered repeatedly in the text at gradually more demanding levels of difficulty * many applications to diverse fields: index theory, foliations, number theory, particle physics, and fundamental quantum theory * rich in proofs, examples and exercises * comprehensive bibliography and index This text is an introduction to the language and techniques of noncommutative geometry at a level suitable for graduate students, and also provides sufficient detail to be useful to physicists and mathematicians wishing to enter this rapidly growing field. It may also serve as a reference text on several topics that are relevant to noncommutative geometry.