In the first part of the monograph, asymptotic diffraction theory develops on the basis of the principle of the local field in the region of the penumbra on the surface of a well-conducting convex body .. The second part deals with the problems of propagation of radio waves in a homogeneous and heterogeneous (layered) atmosphere when taking into account the diffraction around the Earth. The mathematical appendix develops the theory of integral equations used in the text, and provides tables of Airy functions, as well as auxiliary functions used to calculate the distribution of currents. The book presents a collection of original works by the author.