The priority research program Analysis and Numerics for Conservation Laws was funded by the German research foundation Deutsche Forschungsgemeinschaft (DFG) for a period of six years starting in 1997. The diversity of topics, represented in the present book, was one of the strength of the research program. Research groups of very different background, most of which were interacting for the first time, contributed to this interdisciplinary work. The present book contains contributions from interlinked participating projects ranging from the analysis of hyperbolic systems of first order partial differential equations, the development of improved numerical methods for these equations to applications in astrophysics and engineering. It aims at conveying their results achieved in the program to readers outside of their own particular field. The book contains a large number of figures and a number of color plates. The reader can find an up-to-date presentation of many current research topics in the field.