An informative study on the advanced theory of diffraction, the mathematical problem concerning the diffraction by a semi-infinite cone with circular cross section for the Helmholtz equation is here considered for the more general boundary condition of constant impedance type. This book approaches the problem giving due consideration to the issue previously stated by D.S. Jones: the difficulty in obtaining the uniqueness of the solution. An exact analytical method is developed to reduce this problem to the determination of the solution of a well-posed non-oscillatory integral equation, of which the solution can be directly used to express the field in an integral form.