This advanced textbook provides an exhaustive review of topics of immense importance to the fundamental understanding of physics of materials at high pressures. The book presents the current status of experimental and theoretical techniques used to understand the behaviour of materials under high compression. Various topics covered in this book are high pressure studies of materials, equation of state of materials, phase transitions under high pressures, behaviour of hydrogen and hydrides under pressure, and hydrogen bond in solids under high pressure. This book is highly useful reference for the scientists working in the field of condensed matter in general and its behaviour under static and dynamic compression, in particular.