Theory: Electromagnetic Radiation from a Charged Particle in a Crystal - Qualitative Consideration -- Radiation of a Charged Particle in Periodic Media - Classical Theory -- Quantum Electrodynamics in a Crystal -- Experiments and Applications: Characteristics of PXR from Relativistic Electrons -- Special Cases of PXR Generation -- X-Ray Radiation from Nonrelativistic Particles -- Prospective PXR Applications -- Collective Effects in PXR within a High-Current Electron Beam.This systematic and comprehensive monograph is devoted to parametric X-ray radiation (PXR). This radiation is generated by the motion of electrons inside a crystal, whereby the emitted photons are diffracted by the crystal and the radiation intensity critically depends on the parameters of the crystal structure. Nowadays PXR is the subject of numerous theoretical and experimental studies throughout the world. The first part of the book is a theoretical treatment of PXR, which includes a new approach to describe the radiation process in crystals. The second part is a survey of PXR experimental results and the possible applications of PXR as a tool for crystal structure analysis and a source of tunable X-ray radiation.