The book gives an introduction to the fundamental properties of hyperbolic partial differential equations und their appearance in the mathematical modeling of various problems from practice. It shows in an unique manner concepts for the numerical treatment of such equations starting from basic algorithms up actual research topics in this area. The numerical methods discussed are central and upwind schemes for structured and unstructured grids based on ENO and WENO reconstructions, pressure correction schemes like SIMPLE and PISO as well as asymptotic-induced algorithms for low-Mach number flows. The book is mainly written for students from mathematics, physics and engineering but also well suited for researchers from academic institutes and industry.