The theory of radiant energy transfer is the most important branch of theoretical astrophysics. This is due primarily to the fact that radiation transfer plays a huge role in the physical processes occurring in celestial bodies. At the same time, the transfer of radiation in the outer parts of celestial bodies determines the nature of their spectra, which form the basis of astrophysical research. This book describes some new methods in the theory of radiation transfer, as well as the application of these methods to the solution of a number of astrophysical problems. Much attention is paid to the diffusion of radiation with redistribution by frequencies and non-stationary processes of radiation transfer, since these issues have not previously been considered. From the preface: The theory of radiant energy transfer represents the most important section of theoretical astrophysics. This is due primarily to the fact that radiation transfer plays a huge role in the physical processes occurring in celestial bodies. At the same time, the transfer of radiation in the outer parts of celestial bodies determines the nature of their spectra, which form the basis of astrophysical research. With the problem of radiation transfer, we also meet in geophysics (in the study of the earth's atmosphere and water basins) and in some other departments of physics. Recently, the problem of neutron diffusion has acquired great importance, related to the problem of radiation transfer used by metopes..