Since the appearance of the pioneering works by V.L. Ginzburg and N.G. Denisov, who discovered the phenomenon of linear absorption of electromagnetic radiation in an inhomogeneous plasma due to strong plasma resonance in the vicinity of the critical density, the theory of this phenomenon has not received consistent development as applied to strong electromagnetic fields, which are of practical interest today, primarily laser fields. The review is devoted to a systematic presentation of the analytical relativistically nonlinear theory of resonant absorption and harmonic generation of laser radiation in an inhomogeneous plasma under conditions of a significant manifestation of the plasma electron nonlinearity up to laser light intensities at which the motion of electrons in the vicinity of the critical density turns out to be relativistic. Using the methods of modern theory of transformation groups, the review describes: the structure of a nonlinear electromagnetic field in plasma resonance, nonlinear effects of suppression of the resonant absorption coefficient and the angle shift of the resonant absorption curve with increasing laser intensity, the formation of quite smooth spectra of laser light harmonics decaying according to a power law, emitted by the plasma near the breaking threshold of the nonlinear plasma field, as well as the main properties of the electrostatic field generated in the vicinity of the critical density.