A quantum theory of electromagnetic radiation of relativistic particles has been developed with allowance for channelling and thermal vibrations of crystal nuclei. A general formula for the probability of radiation has been derived after averaging over initial and summing over final polarizations of a particle and polarization of photons. Averaging over crystal states of nuclei has been made in both cases: with excitation of phonons and without it. The total radiation has been shown to be formed by channelled and Bremsstrahlung radiations in interrelated way. It has been established that incoherent Bremsstrahlung arises in scattering on thermal vibrations. The particular conditions determining the properties of this radiation in channelling have been derived from the general formula and analyzed.