This book is a systematic investigation into the metaphysical foundations of identity over time. The author elaborates and evaluates the most common theory about the persistence of objects through time and change, namely the classical theory of spatio-temporal continuity. He shows how the theory requires an ontology of temporal parts, according to which objects are made up of temporally extended segments or stages. This ontology is criticized as unwarranted by modern space-time physics, and as internally incoherent. The author argues that identity over time should be seen as a primitive or unanalysable phenomenon, and that the so-called puzzle cases and paradoxes of identity can be dealt with without recourse to such an ontology.