This project deals with the semiclassical approximation for quantum systems which are classically chaotic. The main objective is to develop more general formulas that can take into account various kind of experimental situations, in particular in solid-state physics and atomic physics. To get this result, one will use resummation techniques for semiclassical series, and compute corrections to these formulas (diffractive terms, and terms in higher order in h). Direct applications include semiclassical computation of weak localization in mesoscopic systems, study of the influence of disorder, and calculation of scattering amplitudes for an helium atom. Part of the project will be devoted to classical waves (elasticity) and dynamical systems.