1. Introduction. 2. Linearized Theory - Transonic Breakdown. Equations of Acoustics. Galilean Transformation - Uniform Translation. Slender Body Theory - Acoustics. Exact Equations of Planar Flow; Shock Waves and Entropy Jump. Linearized Theory for Thin Airfoils. 3. Transonic Expansion Procedures; Simple Solutions, Integral Relations. Expansion Procedure for Steady Flow Past Airfoils. Expansion Procedure Applied to the Basic System of Equations. Expansion Procedures for Jet Flows. Transonic Similarity Rules. Hodograph Equations for Planar Flow. Simple Waves, Shock Waves, Detachment. Nozzle Flow, Branch Lines, Limit Lines. Subsonic and Sonic Jets. Transonic Slender Bodies; Expansion Procedure, Area Rule. Lift and Drag Integrals. Unsteady Transonic Flow. 4. Transonic Far Fields. 5. Transonic Airfoil Theory. Problem Formulation. Nose Singularity. Shock Waves at a Curved Surface. Numerical Methods, Physical Plane, Steady Flow. Airfoils at Sonic Velocity. The Stabilization Law. 6. Three Dimensional Wings. 7. Quasi-Transonic Flow. Linearized Theory. Quasi-Transonic Equations. Application to Delta Wing with Wedge Cross-Section. Index.