The purpose of this book is to give an introduction to the theoretical and computational fluid dynamics of a compressible fluid. Emphasis is laid on the basic assumptions and the formulation of the theory of compressible flow as well as on the methods of solving problems. This book is intended for the students of fluid dynamics who are interested in the essential results and the useful techniques in the theoretical analysis and numerical methods of compressible flow. The authors also hope that the book may serve as a useful reference to research workers in this field. After the introduction, the thermodynamical and physical properties of gases are briefly reviewed. These serve as a foundation for the fluid dynamics of compressible fluid. In order to limit the size of this book, we consider main ly the flow of an ideal compressible fluid in which the effects of transport phenomena are neglected (Chapter I to XVI). However, the transport phenomena do have much influence on the flow ofa compressible fluid. Hence in Chapter XVII, some basic concepts of transport phenomena are discussed, which prepare the students for further study of some important aspects of a compressible fluid flow.