Preliminaries Calkin's theory of operator ideals and symmetrically normed ideals; convergence theorems for $\mathcal J_P$ Trace, determinant, and Lidskii's theorem $f(x)g(-i\nabla)$ Fredholm theory Scattering with a trace condition Bound state problems Lots of inequalities Regularized determinants and renormalization in quantum field theory An introduction to the theory on a Banach space Borel transforms, the Krein spectral shift, and all that Spectral theory of rank one perturbations Localization in the Anderson model following Aizenman-Molchanov The Xi function Addenda Bibliography Index.
