In order to focus on the latest trends in theory and numerics in this area of research and to encourage further research in this field, we have decided to organize the “International School of Theory and Numerics of Nature Conservation Laws” at FreiburgjLittenweiler from September 20 until October 24, 1997 The school words promoted DFG Research Training Group “Nonlinear Difference Equations, Modeling, Theory, Numerics, Visualization” at the University of Freiburg. It was attended by around 60 young international researchers. This volume contains the contributions of the five main teachers of the school. Each article includes five hours of lectures on a specific new area of research in the field of theory and numerics for nature conservation laws. There are reviews of recent developments, accompanied by new research by the authors. The topics include a kinetic approach to conservation laws by Benoit Perthame, which can be used to construct approximate Riemann solvers for the entire gas dynamics system. Some ideas for stability and entropy analysis are discussed.