High resolution upwind and centred methods are today a mature generation of computational techniques applicable to a wide range of engineering and scientific disciplines, Computational Fluid Dynamics (CFD) being the most prominent up to now. This textbook gives a comprehensive, coherent and practical presentation of this class of techniques. The book is designed to provide readers with an understanding of the basic concepts, some of the underlying theory, the ability to critically use the current research papers on the subject, and, above all, with the required information for the practical implementation of the methods.  Direct applicability of the methods  include: compressible, steady, unsteady, reactive, viscous, non-viscous and free surface flows. For this third edition the book was thoroughly revised and  contains substantially more, and new material both in its fundamental as well as in its applied parts.