The monograph is devoted to the development of a new approach to statistical theory and some specific results obtained within its framework. The approach is based on the description of the system of many bodies by means of distribution functions dependent on coordinates, velocities, accelerations, the first derivatives of accelerations, and t.. p. On a single basis, filamentous and plate structures are described as excited states of the crystal, the phenomenon of channeling, the effects of shadows and spots of Venus. The last chapter of the monograph is devoted to the construction of covariant statistical equations and some methods of their solution.