There is a history of the creation of the theory of the movement of the moon - for almost 30 centuries, from ancient Babylon to the present day. After the development of methods of celestial mechanics based on Newton's law of universal gravitation, it became clear that the theory of the movement of the moon is one of the most difficult tasks of celestial mechanics, because the "main disturber" of the movement of the moon is the most massive of the bodies of the solar system - the Sun. The exposition is conducted in the form of a story about the works of scientists who contributed to the solution of this difficult task, including Russian and Soviet scientists. The final chapter describes how scientists “taught” computers not only to make calculations on ready-made formulas, but also to derive these formulas according to a given algorithm. The use of computers made it possible to achieve the accuracy of determining the position of the moon in space within a few centimeters. For high school students, teachers and astronomy enthusiasts.