Noncommutative geometry (An introduction to selected topics) (Q1597436)

This is a nice introductory survey of noncommutative geometry. The author starts by showing how the duality (Spaces) \(\leftrightarrow\) (Commutative Algebras) generalizes to (Quotient Spaces) \(\leftrightarrow\) (Noncommutative Algebras). He goes on to discuss the relationship between modules and (vector) bundles, the Connes-Chern character of idempotents, spectral triples, and the noncommutative torus and \(4\)-sphere. Along the way the author talks about applications to various fields. It should be useful as a guide to beginners.