In the book the mathematical methods of nuclear cross sections and phases of elastic scattering, energy and characteristics of bound states in two- and three-particle nuclear systems, when the potentials of interaction contain not only central, but also tensor component, are presented. Are given the descriptions of the mathematical numerical calculation methods and computer programs in the algorithmic language "BASIC" for "Turbo Basic" of firm "Borland" for the computers of the type IBM PC AT. For the numerical solutions of the initial Schroedinger equations are used finite- difference and variational methods, and also method of Runge-Kutta with the automatic calling sequence on the assigned accuracy of results for the scattering phase shifts and binding energy. Is given the description not of the standard methods of solving the system of equations of Schroedinger to the bound states and the alternative to Schmidt's method, method of solution of the generalized matrix problem at the eigenvalues. The developed programs make it possible to determine the wave functions of relative motion of nuclear fragments, calibrated to the correct asymptotic behavior taking into account Coulomb interaction. The programs of the extraction of nuclear phases (phase shift analysis) from the differential elastic cross sections are given. The book can be used as the textbook according to the numerical mathematical methods for the students and the graduate students of the physical and mathematical specialties of higher educational institutions. This Book is written in Russian, but will perhaps present certain interest.