The book presents solutions to a complex of internal and external problems of electromagnetics associated with the development of theory, construction of mathematical models and the development of rigorous methods for calculating the electrodynamic characteristics of combined vibrator-slot structures. The solutions of problems for determining the characteristics of impedance vibrator and slot radiators with arbitrary geometric and electrophysical parameters presented in the monograph were obtained within the framework of the unified methodological approach to construct asymptotic solutions of integral equations on currents and their systems. This approach made it possible to study a number of new combined vibrator-slot structures. The research results reveal the possibilities of using such structures as basic elements in the creation of modern antenna-waveguide devices operating in the ranges from meter to millimeter wavelengths, with new technical characteristics and functional purpose. The book is intended for senior and postgraduate students and researchers working in the fields of radiophysics, radio engineering and antenna-feeder design. The book covers the following topics: * excitation of electromagnetic waves in volumes with coordinate boundaries;* general issues of the theory of thin impedance vibrators and narrow slots in a spatial-frequency representation;* solution of current equations for isolated vibrator and slot scatterers;* combined radiating vibrator-slot structures in rectangular waveguide;* T-junctions of rectangular waveguides with vibrator-slot structures in coupling areas;* waveguide radiation of the combined vibrator-slot structures;* combined vibrator-slot structures located on a perfectly conducting sphere;* combined vibrator-slot Radiators in antenna arrays;* ultrawideband vibrator-slot structures;