These proceedings from the June 2000 conference and instructional symposium include treatments of five expository lectures on noncommutative geometry for mathematicians who were not familiar with the subject, which is to an unusual extent the creation of a single mathematician, Alain Connes. The lectures address an application of non-commutative geometry to topology, discuss Novikov-type conjectures, reason out the residue index theorem of Connes and Moscivici, and relate noncommutative geometry to number theory. Annotation �2007 Book News, Inc., Portland, OR (booknews.com)

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