Main topic of the lecture are modern numerical methods to handle systems of conservation laws as they appear in particular in fluid mechanics. Possible themes are adaptive methods for basic partial differential equations in fluid mechanics, theory and application of heterogeneous multiscale methods, asymptotic-induced methods in limit regimes (weakly compressible, dilute, nearly inviscid fluids,... ), high-order Discontinuous-Galerkin methods, methods for multiphase flow with and without phase transition (phase field modeling, ghostfluid and level-set techniques)