This book covers the basics of noncommutative geometry (NCG) and its applications in topology, algebraic geometry, and number theory. The author takes up the practical side of NCG and its value for other areas of mathematics. A brief survey of the main parts of NCG with historical remarks, bibliography, and a list of exercises is included. The presentation is intended for graduate students and researchers with interests in NCG, but will also serve nonexperts in the field.



Contents
Part I: Basics
Model examples
Categories and functors
C -algebras

Part II: Noncommutative invariants
Topology
Algebraic geometry
Number theory

Part III: Brief survey of NCG
Finite geometries
Continuous geometries
Connes geometries
Index theory
Jones polynomials
Quantum groups
Noncommutative algebraic geometry
Trends in noncommutative geometry