Contents -- Preface -- Equivariant Homology for SL(2) of a p-adic field -- Cyclic homology and the Atiyah-Patodi-Singer index theorem -- K- homology and the index theorem -- On the K-theory proof of the index theorem -- Topology of covers and the spectral theory of geometric operators -- Some applications of cyclic cohomology to the study of group C* -algebras -- Spectral theory for self-adjoint operator extensions associated with Clifford algebras -- Averaging operators and open manifolds -- K-theory and a bivariable Fredholm index