This book, in three parts, describes three phases in the development of the modern theory and calculation of the Moon's motion. Part I explains the crisis in lunar theory in the 1870s that led G.W. Hill to lay a new foundation for an analytic solution, a preliminary orbit he called the 'variational curve.' Part II is devoted to E.W. Brown's completion of the new theory as a series of successive perturbations of Hill's variational curve. Part III describes the revolutionary developments in time-measurement and the determination of Earth-Moon and Earth-planet distances that led to the replacement of the Hill-Brown theory in 1984.