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This text exposes contemporary analytical and semianalytical techniques for solving typical celestial mechanics problems by computer. It presents new algorithms of perturbation theory and helps to develop, on the basis of some general computer algebra systems, specialized software enabling one to construct analytical theories of the motion of celestial objects. Particular attention is paid to applying the elliptic function expansions to economize on the number of terms in the resulting series in problems with large values of parameters. Even problems considered as intractable may now be treated efficiently. The author addresses not only astronomers but also amateurs interested in orbit calculations for celestial objects or satellites. He also develops specialized computer systems and perturbation algorithms to construct a general planetary theory general relativistic lunar theory, for solving typical celestial mechanics problems.