In the proposed project we will deal with mathematical and numerical modelling ofcomplex multi-dimensional systems of hyperbolic conservation laws and balance laws.Models to be studied theoretically as well as experimentally include: nonlinearhyperbolic conservation laws, such as the Euler equations of fluid dynamics, themagnetohydrodynamic equations or the multi-phase flows as well as balance laws, suchas the shallow water equations with source terms modelling the bottom topography andfriction effects. Some other models we shall like to consider are the system ofconservation laws and balance equations governing the evolution of three dimensionalnonlinear wave fronts and shock fronts respectively. Our aim is to use genuinelymulti-dimensional schemes, such as the finite volume evolution Galerkin methods, upwind-based multi-dimensional Boltzmann methods as well asrelaxation schemes. The project is supported from the German AcademicExchange Service (DAAD). Cooperation with the group ofProf. Phoolan Prasad and Dr. S.V. Raghurama Rao from the Indian Institute of Science, Bangalore.