From the reviews: "The book under review provides a self-contained, thorough, and modern account of the mathematical theory of hyperbolic conservation laws. ... gives a detailed treatment of the existence, uniqueness, and stability of solutions to a single conservation law in several space dimensions and to systems in one dimension. This book ... is a timely contribution since it summarizes recent and efficient solutions to the question of well-posedness. This book would serve as an excellent reference for a graduate course on nonlinear conservation laws ... ." (M. Laforest, Computer Physics Communications, Vol. 155, 2003) "The present book is an excellent compromise between theory and practice. Since it contains a lot of theorems, with full proofs, it is a true piece of mathematical analysis. On the other hand, it displays a lot of details and information about numerical approximation for the Cauchy problem. Thus it will be of interest for a wide audience. Students will appreciate the lively and accurate style ... . this text is suitable for graduate courses in PDEs and numerical analysis." (Denis Serre, Mathematical Reviews, 2003 e)