The behaviour of a plane shock, of any strength, travelling along a wall, when it reaches a corner where the wall turns through a small angle $\delta $, is investigated mathematically by use of a linearized theory of anisentropic flow (section section 2 to 5). At a convex corner pure diffraction occurs; at a concave corner Mach reflexion (section 8). The shape of the shock (section 6) and the pressure distribution over the wall (section 7) are calculated for a variety of shock Mach numbers from 1 to $\infty $. The connexion, for weak shocks, with acoustic theory, is displayed (section 9). The work will be used in later parts to assist in a hypothetical description of the flow when $\delta $ is not small.