At flight speeds beyond 30% of the speed of sound, compressibility must be considered in order to accurately describe the behaviour of aircraft. This course first considers the general nature of isentropic expansion and compression of gases in subsonic and supersonic flows. Non-isentropic compression by shock waves in supersonic flow is then considered and discussed. Prandtl-Meyer expansions, shock expansion theory and the method of characteristics are also covered. These studies lead on to the explanation and quantification of the behaviour of airfoils, finite wings, slender bodies and aircraft in compressible subsonic, transonic and supersonic flows.