Introduction.-Notational Conventions.- Functional Analytic.- On Schatten-von Neumann Classes and Trace Class.- Pointwise Estimates for Integral Kernels.- Dirac-Type.- Derivation of the Trace Formula - The Trace Class Result.- Derivation of the Trace Formula - Diagonal Estimates.- The Case n = 3.- The Index Theorem and Some Consequences.- Perturbation Theory for the Helmholtz Equation.- The Proof of Theorem 10.2: The Smooth Case.- The Proof of Theorem...