The monograph is devoted to various physical phenomena and properties of compressed and heated matter at high energy densities .. Methods of generation, diagnostics, as well as theoretical methods for describing the behavior of a substance at extremely high pressures and temperatures obtained in laboratory and quasi-laboratory conditions are considered. The states of matter with high energy densities that arise at different stages of the evolution of astrophysical objects under the influence of gravity and thermonuclear energy emission are discussed. An attempt is made to systematize, summarize and present from a single point of view an extensive theoretical and experimental material relating to a new field of science - the physics of high energy densities .. The book is based on lectures given by the author at the Moscow Institute of Physics and Technology, at the Higher School of Physics of the Ministry of Atomic Energy of Russia, as well as review and invited reports at scientific conferences and symposia .. The book can be useful to a wide range of scientists, graduate students and students of natural sciences, gives them access to original works and allows them to navigate the fascinating problems of modern physics.