The book is based on lectures given by the author at the Higher School of Physics, organized by the Rosatom State Corporation, at the Moscow Institute of Physics and Technology, as well as materials from scientific conferences and symposia. In the course of lectures, diverse physical phenomena and properties of substances in extreme conditions are discussed. Ways to generate , Diagnosis, theoretical methods for describing the behavior of a substance at extremely high pressures and temperatures , as well as the state of a substance with high energy densities, occurring at different stages of the evolution of astrophysical objects under the influence of gravity and thermonuclear energy release . This electronic edition was prepared on the basis of the printed edition of the same name, published in the Publishing House of MPEI in 2013. The book can be useful to a wide range of scientists, graduate students and students of natural sciences, giving them access to original works and allowing them to navigate the fascinating problems of modern physics of extreme states of matter.