Examines the debate in early modern philosophy over the composition and internal architecture of matter, focussing on problems concerning the structure of continua, the metaphysics of parts and wholes, and the individuation of material beings. Are the parts of material bodies actual or potential entities? Is matter divisible to infinity? Do material bodies resolve to atoms? All the leading figures of the period address this cluster of issues, including Galileo, Descartes, Hobbes, Leibniz, Newton, Hume, Boscovich, Reid, and Kant. Presents a historical and critical study of these discussions, and offers an overarching interpretation of the controversy. Locates the central problem in the tension between the early moderns’ actual parts ontology on the one hand, and the programme of the geometrization of nature on the other.