This book offers a fresh interpretation of Leibniz’s theory of substance, taking as starting point his claims that he introduced his monads to solve the problem of the composition of the continuum. It is argued that they can only perform this function if they are understood as requisites for each of the actual parts into which matter is divided, and as sources of the actions distinguishing and making actual these parts. Bodies are not composed of monads, but presuppose them for their reality; and motions are not composed of monadic states, but presuppose their tendencies to change and resist changes. This comprises an original contribution to mereology, which is given a formal rendering using Leibniz’s own logical concepts and notation. The reading is supported by a thorough analysis of the development of Leibniz’s thought, showing how his embodied monads emerge from his long dalliance with atomism, and how his doctrine of dominant and subordinate monads derives from his immersion in the scholastic tradition of the Plurality of Forms, as he seeks to preserve the role of substantial forms in enacting God’s providential plans in a way compatible with a thoroughgoing mechanism. New insight is offered into Leibniz’s construal of bodies and motions as phenomena, his simultaneous advocacy of simple and corporeal substances, his attempt to provide a theory of substantial bonds, the status of passive force in his dynamics, his endorsement of continuous creation and the discreteness of change, and the status of monadic states as momentary.