This book presents a complete proof of Alain Connes Index Theorem generalized to foliated spaces. Connes result is itself an abstraction of the Atiyah-Singer index theorem to the context of foliated manifolds. The book brings together the necessary background from analysis, geometry, and topology. It thus provides a natural introduction to some of the basic ideas and techniques of noncommutative topology. The present edition has improved exposition, an updated bibliography, an index, and additional material covering new developments and applications since the first edition appeared.

Introduction; 1. Locally traceable operators; 2. Foliated spaces; 3. Tangential cohomology; 4. Transverse measures; 5. Characteristic classes; 6. Operator algebra; 7. Pseudodifferential operators; 8. The index theorem; Appendices.

Calvin C. Moore received his Ph.D. from Harvard in 1960 under George Mackey in topological groups and their representations. His research interests have extended over time to include ergodic theory, operator algebras, and applications of these to number theory, algebra, and geometry. He spent from 1960-61 as Postdoc at the University of Chicago and has been on UC Berkeley Mathematics faculty since 1961. He was co-founder (with S. S. Chern and I. M. Singer) of the Mathematical Sciences Research Institute, and has held various administrative posts within the University of California. He is a Fellow of the American Association for the Advancement of Sciences and the American Academy of Arts and Sciences.