The book is devoted to exploring the foundations of the theory of thin impedance vibrator antennas. The text provides a continuation of the classic theory of thin perfectly conducting vibrators. Many consider impedance conception one of the most universal models in the theory of wave processes, as it informs such a wide spectrum of uses in solving practical problems of electrodynamics. This topic provides an opportunity to further search analytical solutions, allowing a simplification of the mathematical formulation of the boundary problem. The theory strives to widen the boundaries of the impedance vibrator antennas application in complex modern radio-and-electronic systems and devices. The results of much original research conducted by the authors will be useful for practicing engineers and designers of antenna and waveguide systems.The book is written in an academic style, and can be used to teach students and post graduates about radiotechnical and radiophysical specialities. The conclusion of the book lists many actual applied problems, which can provide inspiration for several potential PhD projects.Topics covered in this book are:•general questions of the theory of impedance vibrators in the spatial-frequency representation•electromagnetic waves radiation by impedance vibrators in free space and material mediums•electromagnetic waves radiation by impedance vibrators in material mediums over the perfectly conducting plane•electromagnetic waves scattering by irregular impedance vibrators in free space•generalized method of induced electromotive forces for investigation of the characteristics of impedance vibrators•radiation of electromagnetic waves by radial impedance vibrators on the perfectly conducting sphere•electromagnetic waves scattering by impedance vibrators in the rectangular waveguide