The subject of this book, traditionally called celestial mechanics, is the oldest branch of theoretical physics. The publication in 1687 of the Principia, Newton’s masterpiece on celestial mechanics, is widely regarded as the capstone of the Scientific Revolution. Since then, celestial mechanics has attracted the attention of many of the greatest physicists and mathematicians of the past several centuries, including Lagrange, Laplace, Gauss, Poincar ́e, Kolmogorov, and others. Concepts first explored in celestial mechanics are central to many if not most branches of physics, and its successful high-precision predictions of the motions of the planets have impacted disciplines as diverse as navigation and philosophy.