Unique in its emphasis of both the mathematical and physical aspects of compressible flows, this book presents its subject matter in an increasing order of complexity, starting from simple one-dimensional flows through quasi one-dimensional flows to oblique shocks and Prandtl Meyer flow. This treatment interweaves mathematical development of the concepts and physical insights. Worked examples and exercise problems have been drawn from practical applications in propulsion and gas dynamics. These are comprehensive and are formulated to test the understanding of the subject matter, thus serving as a self-check for the reader.