Everything in the universe rotates: the meteors, the asteroids, the planets and their satellites, the sun, the stars, the clusters and nebulae, even the galaxies themselves. The problem of the shape of a rotating body is therefore universal in astronomy. Its treatment in this book, which deals with the figures of equilibrium and distortions of rotating bodies, is full and rigorous. Suitable for upper-level undergraduates and graduate students, this text was written by a renowned researcher and educator who taught at Columbia University and served for many years as a research associate at the Lamont-Doherty Earth Observatory. The first six chapters encompass the most exact methods used in the theory of figures of equilibrium and their most important results. Discussions cover the methods of Poincaré, Liapounov, Lichtenstein, and Wavre. The second part examines other problems concerning the figures of celestial bodies: invariable or varying figures, zonal rotation, systems composed of fluid and rigid parts, fluid mass and centers of attraction, and figures of compressible masses.