Image theory, previously developed for the analysis of a conducting half plane by the present authors, is extended to problems involving a conducting wedge. It is shown that the classical two-dimensional electromagnetic field problem of a perfectly conducting wedge can be solved by interpreting the contribution due to the wedge as arising from a suitably defined image source consisting of a discrete and a continuous part located in complex space. The image currents give the exact field, do not depend on the point where the field is calculated and can be expressed in terms of simple trigonometric functions in contrast to more complicated functions characterizing the physical surface currents on the wedge or non-physical approximate currents applied in the Physical Diffraction Theory. Also, the image theory applies to the corner reflectors of any corner angle. The classical image theory with discrete images for corner angles of the form π/n is obtained as a special case.