This introduction to unsteady aerodynamics provides a general background to illustrate current linearised theoretical methods. It includes an opening section to remind the user of the basic principles that underline linearised theory. This leads on to various methods of solution for aerofoil sections (two-dimensions) and wings (three-dimensions) oscillating in simple harmonic motion in both subsonic and supersonic flow. The practicalities of semi-empirical methods and the applications of unsteady aerodynamics to flutter, atmospheric disturbances and active control systems are also discussed.