Fast development of the synchrotron facilities opens a new era in X-ray optics where the diffraction, spectroscopic and time-resolved methods are combined in one experiment. Near-X-ray absorption edges the strong magnetic and anisotropic effects to reveal itself. As a result, the X-ray reflectivity method has acquired new possibilities: in previous times it gave the information only about the electronic density profiles in thin films, but nowadays it detects the magnetic and electronic depth-profiles. The theoretical foundations of the method need to be developed accordingly. The textbook presents the first systematic exposition of the new X-ray optics, including the effects of anisotropy in X-rays scattering near the absorption edges or nuclear resonance (Mössbauer) scattering. The book may be useful for students and postgraduates of physical specialties, as well as for researchers of magnetic multilayers conducting experiments with synchrotron radiation.