The monograph presents a comparative analysis of various thermodynamic models of state equations. The main ideological prerequisites of theoretical methods and experiment are considered. The main focus is on the description of states , of greatest interest to high energy density physics, which has already been received.... or in the foreseeable future can be obtained under controlled conditions on Earth or are realized in astrophysical objects at different stages of their evolution. Also considered are ultra-extreme astrophysical and nuclear physics applications, where the thermodynamics of matter is significantly influenced by relativism, powerful gravitational and magnetic fields, thermal radiation, nuclear particle transformation, neutronization of nucleons, and quark deconfinement. For a wide range of specialists dealing with the equations of state of matter and high energy density physics, as well as for undergraduate and graduate students .