In the framework of the Hartree-Fock-Bogolyubov method, the nuclear problem of many bodies is solved. Phonon operators, including neutron-proton ones, are introduced, and the approximation of chaotic phases for states of electric and magnetic types is presented. General diagram of bosonic representation of fermionic operators is given. A collective Hamiltonian for quadrupole excitations in the SU (6) -apposition is constructed. Mathematical apparatus of interacting bosons model is described. A quasi-partial phonon model of the nucleus is formulated, designed to describe the low-quasiparticle components of wave functions at low, medium and high excitation energies. The structure of non-rotational states of deformed and spherical nuclei with energy less than neutron binding energy is described.