Abstract
These lectures discuss topics in the theory of hyperbolic systems of conservation laws focusing on the mathematical theory of fluid-dynamic limits. First, we discuss the emergence of the compressible Euler equations for an ideal gas in the fluid-dynamic limit of the Boltzmann equation or of the BGK model. Then we survey the current state of the mathematical theory of fluid-dynamic limits for BGK systems and for discrete velocity models of relaxation type. This is done for the case that the limit is a scalar conservation law or a system of two equations.