Front Tracking for Hyperbolic Conservation Laws Preface Introduction Scalar Conservation Laws A Short Course in Difference Methods Multidimensional Scalar Conservation Laws The Riemann Problem for Systems Existence of Solutions of the Cauchy Problem Well Posedness of the Cauchy Problem Total Variations Compactness etc. The Method of Vanishing Viscosity Answers and Hints References Index. . Hyperbolic conservation laws are central in the theory of nonlinear partial differential equations and in science and technology. The reader is given a self contained presentation using front tracking which is also a numerical method. The multidimensional scalar case and the case of systems on the line are treated in detail. A chapter on finite differences is included. From the reviews: It is already one of the few best digests on this topic. The present book is an excellent compromise between theory and practice. Students will appreciate the lively and accurate style. D. Serre MathSciNet I have read the book with great pleasure and I can recommend it to experts as well as students. It can also be used for reliable and very exciting basis for a one semester graduate course. S. Noelle Book review German Math. Soc. Making it an ideal first book for the theory of nonlinear partial differential equations...an excellent reference for a graduate course on nonlinear conservation laws. M. Laforest Comp. Phys. Comm.