ESDU AERO S.00.03.06 defines some of the expressions and quantities that occur frequently in calculations related to high-speed flow and summarises the basic thermodynamic concepts. Equations for such quantities as internal energy, entropy, enthalpy, speed of sound, maximum velocity, and kinetic pressure are treated. The standard expression relating pressure and temperature in isentropic flow is derived and used to obtain equations for the ratios of such flow parameters as temperature and pressure to those at stagnation conditions. Sutherland's formula for the variation of dynamic viscosity with temperature is given and equations for one-dimensional isentropic flow developed including that relating the cross-sectional area to that at the throat. For supersonic flow the concept of Mach lines is introduced together with expansion and compression waves. The concepts of the Prandtl-Meyer expansion and the method of characteristics are introduced. The physical phenomena of shock waves are discussed. Throughout reference is made to other ESDU documents that provide data on, for example, flow properties through plane and conical shocks, and the variation of isentropic flow stagnation conditions with Mach number.