Noncommutative geometry : lectures given at the C.I.M.E. summer school held in Martina Franca, Italy, September 3-9, 2000

This English version of the path-breaking French book on this subject gives the definitive treatment of the revolutionary approach to measure theory, geometry, and mathematical physics developed by Alain Connes. Profusely illustrated and invitingly written, this book is ideal for anyone who wants to know what noncommutative geometry is, what it can do, or how it can be used in various areas of mathematics, quantization, and elementary particles and fields.First full treatment of the subject and its applicationsWritten by the pioneer of this fieldBroad applications in mathematicsOf interest across most fieldsIdeal as an introduction and surveyExamples treated include: the space of Penrose tilingsthe space of leaves of a foliationthe space of irreducible unitary representations of a discrete groupthe phase space in quantum mechanicsthe Brillouin zone in the quantum Hall effectA model of space time