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

From the Back Cover

Developed by Alain Connes, noncummutative geometry is the set of tools and methods that makes possible the classification and analysis of a broad range of objects beyond the reach of classical methods. This English version of the path-breaking French book on the subject gives the definitive treatment of his revolutionary approach to measure theory, geometry, and mathematical physics. 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.

"About this title" may belong to another edition of this title.

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