The book deals with the construction of algorithms for accurate numerical prediction of the movement of celestial bodies based on the use of numerical methods of high orders and transformations that regularize and stabilize the equations of motion. The monograph describes the Runge-Kutta methods of high orders, the Taylor decomposition method, the implicit single-step Everhart algorithms, extrapolation methods, multi-step methods that take into account the properties of motion, the method of multi-turn integration. Numerous examples show the efficiency in the problems of celestial mechanics of numerical methods of high orders in combination with regularizing and stabilizing transformations of the equations of motion of celestial bodies. The book is designed for specialists in celestial mechanics and astrodynamics, as well as for graduate students and senior students of physical and mathematical faculties of universities specializing in celestial mechanics and space flight mechanics.