Riemann-Roch Theorem and Index Theorem in Non-commutative Geometry

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In this lecture we review apprearance of the Riemann-Roch Theorem in classical function theory, Algebraic topology, in theory of pseudo-differential operators and finally in noncommutative geometry. We show also it usefulness in many problem of quantization and harmonic analysis on Lie groups.
27pages, latex, no figure

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