Noncommutative Geometry

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 applications

• Written by the pioneer of this field

• Broad applications in mathematics

• Of interest across most fields

• Ideal as an introduction and survey

• Examples treated include:

• the space of Penrose tilings

  the space of leaves of a foliation

  the space of irreducible unitary representations of a discrete group

  the phase space in quantum mechanics

  the Brillouin zone in the quantum Hall effect

  A model of space time

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