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 deeperinsights 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 subjectand closely related topics; the contributions in this volume include the four main lectures, cover advanced developments and are delivered by prominent specialists.

This book contains a collection of articles provided by the participants of the SFB-workshop on C*-algebras, March 8 - March 12, 1999 which was held at the Sonderforschungsbereich "Geometrische Strukturen in der reinen Mathematik" of the University of Munster, Germany. The aim of the workshop was to bring together leading experts in the theory of C* -algebras with promising young researchers in the field, and to provide a stimulating atmosphere for discussions and interactions between the participants. There were 19 one-hour lectures on various topics like - classification of nuclear C*...