This book is devoted to the theme of crystallographic studies at high pressure, with emphasis on the phenomena characteristic to the compressed state of matter, as well as experimental and theoretical techniques used to study these phenomena. As a thermodynamic parameter, pressure is remarkable in many ways. In the visible universe its value spans over sixty orders of magnitude, from the non-equilibrium pressure of hydrogen in intergalactic space, to the kind of pressure encountered within neutron stars. In the laboratory, it provides the unique possibility to control the structure and properties of materials, to dramatically alter electronic properties, and to break existing, or form new chemical bonds. This agenda naturally encompasses elements of physics (properties, structure and transformations), chemistry (reactions, transport), materials science (new materials) and engineering (mechanical properties); in addition it has direct applications and implications for geology (minerals in deep Earth environments), planetary sciences, biology and medicine.