The principles of the differential theory of light diffraction are presented in cylindrical coordinates. Special attention is played to the factorisation rules necessary to obtain faster convergence with respect to the number of basic functions used in the field representation. A detailed description is given for diffracting objects having rotational symmetry and finite cylindrical length. Some properties of light diffracted by a single circular aperture piereced in a finitely conducting screen are discussed, including the excitation of surface plasmon wave and the enhanced beaming.