This book is the first to give a comprehensive presentation of the modern approach to numerical simulation of supersonic and hypersonic flows around bodies. In its use of the viscous gas dynamics equations throughout the computational domain, the main advantage of the approach presented is that it takes account of the important effects of rarefaction, viscous-inviscid interaction, separation, chemical and thermal non-equilibria, and radiation. A number of example calculations are given, demonstrating the application of the viscous shock layer models to a wide range of modern gas dynamics problems. Audience: Researchers into supersonic and hypersonic gas dynamics. Suitable for those already familiar with the fundamentals of gas dynamics, the physics of high-temperature gases and finite-difference numerical methods. Also suitable for graduate and postgraduate courses on computational gas dynamics and heat transfer.