The basics of designing antenna systems are outlined. General concepts of electrodynamics and electromagnetic field theory are given in relation to the solution of electrodynamic problems of antenna theory. The main numerical methods of solution are considered, such as projection methods, method of finite differences, method of finite elements and method of integral equations. The basic theoretical information necessary for numerical analysis of antennas using packages of application programs MWO, HFSS and EDEM is presented. The main provisions of the theory of wire and microstrip antennas, which have wide practical application for communication systems, are considered.