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In this chapter the results of theoretical and experimental studies of the interaction of an electromagnetic field with a plasma (fundamental interaction of the wave-particle type) both in the regime of standing waves (in the case of a resonator) and in the case of traveling waves in a waveguide are presented. The results of computer modeling the distribution of a regular electromagnetic field for various designs of electrodynamic structures are considered. The most attractive designs of electrodynamic structures for practical application are determined. A brief review and analysis of some mechanisms of stochastic plasma heating are given as well as the conditions for the formation of dynamic chaos in such structures are determined. Comparison analysis of microwave plasma heating in a regular electromagnetic field (in a regime with dynamical chaos) with plasma heating by random fields is considered. It is shown, that stochastic heating of plasma is much more efficient in comparison with other mechanisms of plasma heating (including fundamental interaction of the wave-wave type). The results obtained in this work can be used to increase the efficiency of plasma heating as well as to develop promising new sources of electromagnetic radiation in the microwave and optical ranges.