Synopsis   Hyperbolic systems of partial differential equations describe a variety of physical phenomena, including gas dynamics, magnetohydrodynamics, and elasticity. These nonlinear systems typically require numerical methods for their solution-methods based on the fundamental properties of hyperbolic systems. Although some reliable methods are well developed , their extension to more complicated hyperbolic systems is not at all straightforward. It requires proper mathematical justification of solution uniqueness, a formulation of the selection principles for relevant solutions, and investigation of their physical admissibility. Most high-resolution methods for gasdynamic equations use Riemann problem solutions to determine fluxes through numerical cell boundaries. Similar methods are expected to be developed for other types of hyperbolic systems, and this book provides the background needed to meet that challenge.Mathematical Aspects of Numerical Solution of Hyperbolic Systems investigates a number of such problems and describes numerical methods based on their analysis. For some systems, it presents the authors' results on the existence and uniqueness of self-similar solutions, which can be used in the development of discontinuity-capturing, high-resolution numerical methods. The authors illustrate their work with a number of numerical and analytical solutions from various applications, and purposely present all analytical results from the viewpoint of their possible application to constructing numerical methods.Motivated by a gap between a fast development of numerical methods and achievements in nonlinear mechanics, this work systematizes and gives a scientific instrumentto overcome the difficulties inherent in the solution of hyperbolic systems. In addition to those interested the development of numerical methods, this important work will prove valuable to physicists and mechanicists who use numerical methods to solve increasingly complicated nonlinear equations