The history of the creation of the theory of the motion of the moon is traced - for almost 30 centuries, from Ancient Babylon to the present day. After developing methods of celestial mechanics based on Newton's law of gravity, it became clear that the theory of motion of the moon - one of the most difficult tasks of celestial mechanics, because the "main troublemaker" of the motion of the moon is the most massive of the bodies of the solar system - Sun. The presentation is in the form of a story about the work of scientists who contributed to solving this difficult task, including Russian and Soviet scientists. The final chapter tells how scientists "taught" computers not only to make calculations using ready-made formulas, but also to derive these formulas using a given algorithm. The use of computers made it possible to achieve accuracy in determining the position of the moon in space within a few centimeters. For high school students, teachers and astronomy lovers.