The most influential work of ancient astronomy is the Almagest of Ptolemy (fl. 2nd century AD). But that work does not tell us everything about its author's views regarding the heavens. Sometime after completing it, Ptolemy turned his attention to giving a physical account of celestial motion. The result is his most important cosmological work, the Planetary Hypotheses, a bold attempt to provide a celestial physics that coheres with the mathematical account of astronomical observations in his Almagest. This book provides the first complete critical edition and English translation of the Arabic version of the Planetary Hypotheses, which is partially lost in its original Greek. It furthermore provides ample commentary on the whole work, which situates the Planetary Hypotheses within the context of its time and investigates philosophical ideas central to the work. These include the epistemic value of mathematics relative to natural philosophy, and the shape, number, and dynamics of the celestial bodies. The book also investigates the influence of the Planetary Hypotheses on a wide range of medieval Arabic astronomical and philosophical works from the 9th to the 13th century AD. The upshot is to establish the Planetary Hypotheses as a crucial text for understanding the history of philosophy and science from Greek antiquity to the Arabic Middle Ages.