Semi-classical approximation in quantum mechanics. A survey of old and recent mathematical results

In this survey the following topics are considered. 1. Propagation of quantum and classical observables. How can the classical evolution be recovered from the quantum evolution? 2. Time dependent WKB approximations. 3. Trace formulas and eigenvalue asymptotics. 4. Quantum signature of classical chaos. 5. Scattering states, limiting absorption principle, asymptotics for the spectral shift function (scattering phase). 6. Propagation of coherent states or wave packets. (orig.)