The philosophical problem of identity and the related problem of change go back to the ancient Greek philosophers and fascinated later figures including Leibniz, Locke, and Hume. Heraclitus argued that one could not swim in the same river twice because new waters were ever flowing in. When is a river not the same river? If one removes one plank at a time when is a ship no longer a ship? What is the basic nature of identity and persistence? In this book, Andre Gallois introduces and assesses the philosophical puzzles posed by things persisting through time. Beginning with essential historical background to the problem he explores the following key topics and debates: mereology and identity, including arguments from 'Leibniz's Law' the constitution view of identity the 'relative identity' argument concerning identity temporary identity four-dimensionalism, counterpart and multiple counterpart theory supervenience the problem of temporary intrinsics the necessity of identity Indeterminate identity presentism criteria of identity conventionalism about identity. Including chapter summaries, annotated further reading and a glossary, this book is essential reading for anyone seeking a clear and informative introduction to and assessment of the metaphysics of identity.