Analytical theories of the motion of the moon

New results have been obtained in connection with the development of analytical theories about the moon. The new results were derived by making use of techniques of algebraic manipulation involving the employment of computers. It is predicted that, in the long run, the techniques will have a very substantial effect on celestial mechancs. With the coming of the space age, the construction of a theory of the motion of the moon at the level of accuracy of the new observations became a challenge for scientists in the area of celestial mechanics. For several years, the work in this field was almost exclusively directed towards the solution of the so-called Main Problem, involving the three body problem earth, moon, and sun. A review is provided of the present status of the solution of the Main problem, and attention is given to new results published about perturbations caused by the oblateness of the earth (and moon) and by the planets. The new results make it possible to test the accuracy of recently proposed analytical theories.