||The monograph is devoted to the exposition of the foundations of modern quantum theory of a solid body with the help of language псевдопотенциала. It is shown that the ideas псевдопотенциала appear as a natural result of the application of the quantum-mechanical scattering theory (described in the book) to the problem of the interaction of an electron from an atom (ion). Special attention is paid to the principles of building a crystalline potentials and the theory of shielding. In the language of the псевдопотенциала the basic principles of the band theory and analyzed the relationship between theory псевдопотенциала and the basic methods of calculation of the energy band structure (OPV, PPV, KKR, ККРЗ). As an example of using the theory of псевдопотенциала discussed its application to one of the actual problems of the theory of phase transformations - the problem of comparative stability of crystalline structures of metals and alloys. On a broad material shows the possibilities of the theory of псевдопотенциалов in this aspect.