2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/65547In 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 figureOperator AlgebrasK-Theory and HomologyQuantum AlgebraRepresentation TheoryRiemann-Roch Theorem and Index Theorem in Non-commutative Geometrytext