The series of expository lectures intended to introduce key topics in noncommutative geometry to mathematicians unfamiliar with the subject. Topics: applications of noncommutative geometry to problems in ordinary geometry and topology, Riemann hypothesis and the possible application of the methods of noncommutative geometry in number theory, residue index theorem of Connes and Moscovici, etc.
This book presents to an audience of graduate students and researchers a modern account of the subject and its applications. The algebraic approach allows the theory to be developed in a general form of wide applicability.
This volume collects the lecture series given at the International Workshop on Noncommutative Geometry that took place at the Institute for Studies in Theoretical Physics and Mathematics in 2005.
