Noncommutative Geometry [electronic resource] : Lectures given at the C.I.M.E. Summer School held in Martina Franca, Italy, September 3-9, 2000 / by Alain Connes, Joachim Cuntz, Erik Guentner, Nigel Higson, Jerome Kaminker, John E. Roberts ; edited by Sergio Doplicher, Roberto Longo.

Cyclic Cohomology, Noncommutative Geometry and Quantum Group Symmetries -- Cyclic Theory and the Bivariant Chern-Connes Character -- Group C*-Algebras and K-Theory -- Geometric and Analytic Properties of Groups -- More Lectures on Algebraic Quantum Field Theory.

Noncommutative Geometry is one of the most deep and vital research subjects of present-day Mathematics. Its development, mainly due to Alain Connes, is providing an increasing number of applications and deeper insights for instance in Foliations, K-Theory, Index Theory, Number Theory but also in Quantum Physics of elementary particles. The purpose of the Summer School in Martina Franca was to offer a fresh invitation to the subject and closely related topics; the contributions in this volume include the four main lectures, cover advanced developments and are delivered by prominent specialists.