The book deals with the numerical solution of equations describing motion of compressible fluids. Classical as well as modern numerical schemes are summarized here. At the beginning, the governing equations are determined and the mathematical problems are defined. Some theoretical results, such as existence and uniqueness of solutions, are mentioned. The main part of the book is concerned with the numerical solution of inviscid as well as viscous compressible flows. Applications of various numerical methods (finite volume method, finite element method, discontinuous Galerkin method and their variants) for the Euler and Navier-Stokes equations are discussed. Convergence properties of numerical schemes are mostly derived for a scalar nonlinear convection-diffusion equation. Several types of mesh adaptation techniques are presented as well. In the book the reader can find a lot of numerical examples demonstrating the efficiency of described methods. The book is suitable for researchers as well as for students dealing with the numerical solution of compressible flows.