This is the first exposition of the quantization theory of
singular symplectic (Marsden-Weinstein) quotients and their
applications to physics. The reader will acquire an introduction to
the various techniques used in this area, as well as an overview of
the latest research approaches. These involve classical
differential and algebraic geometry, as well as operator algebras
and noncommutative geometry. Thus one will be amply prepared to
follow future developments in this field.
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