This book announces a mathematical theory of the internal constitution of stars, and the sources of stellar energy according to the General Theory of Relativity. This is an alternative to the conventional theory of gaseous stars which was introduced in the 1920’s on the basis of classical mechanics and thermodynamics. In contrast, the common consideration of a star and its field according to the General Theory of Relativity, that presented in this book, comes to the model of liquid stars. Such a star is homogeneous inside, with a tiny core (about a few kilometres in the radius) in the centre. The core is selected from the main mass of the star by the collapse surface with the radius according to the star’s mass. Despite almost all mass of the star is located outside the core (the core is not a black hole), the force of gravity approaches to infinity on the surface of the core due to the inner space breaking of the star’s field therein. The super-strong force of gravity is sufficient for the transfer of the necessary kinetic energy to the lightweight atomic nuclei of the stellar substance, so that the process of thermonuclear fusion begins. The energy produced by the thermonuclear fusion is that energy which the stars shine: the tiny core of each star is its luminous “inner sun”, while the produced stellar energy is then transferred to the physical surface of the star due to the thermal conductivity. A new classification of stars is introduced according to the space breaking of their fields: the regular stars (in the range from the dwarfs to the super-giants), Wolf-Rayet stars, neutron stars (and pulsars), and black holes are considered. The introduced liquidmodel matches with the new observational evidences for the state of condensed matter inside stars; in particular, that the Sun consists of the high temperature liquid metallic hydrogen.