Book excerpt: This work should serve as an introductory text for graduate students and researchers working in the important area of partial differential equations with a focus on problems involving conservation laws. The only requisite for the reader is a knowledge of the elementary theory of partial differential equations. Key features of this work include: Broad range of topics, from the classical treatment to recent results, dealing with solutions to 2-D compressible Euler equations Good review of basic concepts (1-D Riemann problems) Concrete solutions presented, with many examples, over 100 illustrations, open problems, and numerical schemes Numerous exercises, comprehensive bibliography and index Appeal to a wide audience of applied mathematicians, graduate students, physicists, and engineers Written in a clear, accessible style, the book emphasizes more recent results that will prepare readers to meet modern challenges in the subject, that is, to carry out theoretical, numerical, and asymptotical analysis.