Probing matter with beams of photons, neutrons and electrons provides the main source of information about both the microscopic and macroscopic structure of materials. This is particularly true of media, such as crystals and liquid crystals, that have a periodic structure. This book discusses the interaction of waves (which may represent x-rays, gamma rays, electrons, or neutrons) with various kinds of ordered media. After two chapters dealing with exact and approximate solutions to the scattering problem in periodic media in general, the author discusses: the diffraction of Moessbauer radiation in magnetically ordered crystals; the optics of chiral liquid crystals; the radiation of fast particles in regular media (Cherenkov radiation); nonlinear optics of periodic media; neutron scattering in magnetically ordered media; polarization phenomena in x-ray optics; magnetic x-ray scattering; and Moessbauer filtration of synchrotron radiation.