Besides, today it is often no longer possible to start very low and, in one or two comprehensive volumes, end up at the frontiers of current research. Hence many of the later volumes are more specialized and more advanced. In this book, the Atiyah-Singer index theorem for Dirac operators on compact Riemannian manifolds and its more recent generalizations receive simple proofs. The main technique which is used is an explicit geometric construction of the heat kernels of a generalized Dirac operator. The first four chapters could be used at the text for a graduate course on the applications of linear elliptic operators in differential geometry and the only prerequisites are a familiarity with basic differential geometry.
Several chapters deal with other preparatory material.