Supersymmetry and index theory

The author presents information mainly concerned with the fact that many of the ingredients and results in index theory have very simple analogs in supersymmetric quantum mechanical systems so that using elementary quantum mechanics one can obtain new proofs of the Atiyah-Singer index theorem and related results. Simple ideas on index theorems and characteristic classes are reviewed; simple results on fermion functional integrals are outlined; supersymmetric quantum mechanical systems which appear naturally in dealing with index problems are analyzed; proof of the classical index theorem is presented; the character valued index theorem is derived; and applications of the methods developed here for the computation of anomalies are presented