Introductory concepts. Recap of the kinetic theory of gases. Elements of thermodynamics. Transport properties of fluids: viscosity, conductivity and diffusivity. Concept of compressibility and compressibility condition. Forces acting on a body immersed in a flow. Inviscid flow. Integral form of the conservation laws. Differential form of the equations. Potential equation. Crocco's theorem. One-dimensional flow. Speed of sound and Mach number. Normal shock equations. Propagation of shock waves. Rayleigh flow. Fanno flow. Oblique waves in supersonic flows. Mach lines. Method of characteristics. Epicycloid. Prandtl-Meyer expansion. Oblique shock wave. Shock Polar. Pressure-deflection diagram. Reflection and intersection of oblique shocks. Shock detached from a bluff body. Reflection of expansion waves. Shock-expansion interaction. Quasi-one-dimensional flow. Flows in nozzles and diffusers. Flow in a supersonic wind tunnel. Unsteady motion of a wave. Normal shock waves in motion. Shock tube. Linearized equation of the potential. Linearized subsonic flow. Linearized supersonic flow. Critical Mach number. Thin profiles in supersonic flows. Transonic flow. Body of minimum wave drag. Area rule. Aerodynamic characteristics of airfoils and wings in compressible flows. Two-dimensional wedges, cones and slender bodies. Effects of viscosity and conductivity. Governing equations. Equations for the thermal boundary layer. Couette flow. Energy equation solutions. Reynolds' analogy. Turbulent thermal boundary layer. Correction of the friction coefficient due to the compressibility and the wall temperature. Heat flux on leading edges of cylindrical and spherical bodies. Hypersonic flows. Physical aspects. "Newtonian" theory. Chemical equilibrium for a mixture of gases at high temperature. Chemical processes downstream of a normal shock and in the boundary layer.