This publication presents an creation to noncommutative geometry and provides a few its fresh purposes to particle physics. it really is meant for graduate scholars in mathematics/theoretical physics who're new to the sector of noncommutative geometry, in addition to for researchers in mathematics/theoretical physics with an curiosity within the actual purposes of noncommutative geometry. within the first half, we introduce the most recommendations and strategies through learning finite noncommutative areas, supplying a “light” method of noncommutative geometry. We then continue with the final framework via defining and interpreting noncommutative spin manifolds and deriving a few major effects on them, corresponding to the neighborhood index formulation. within the moment half, we exhibit how noncommutative spin manifolds certainly supply upward push to gauge theories, using this precept to precise examples. We accordingly geometrically derive abelian and non-abelian Yang-Mills gauge theories, and at last the complete usual version of particle physics, and finish by way of explaining how noncommutative geometry may well point out easy methods to continue past the traditional version.
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