First I’ll introduce the analysis of identity in terms of indiscernibility and then I’ll explain why indiscernibility fails as a sufficient condition, focusing on a famous argument from Max Black which I consider decisive. Then I will move on to the notion that indiscernibility is necessary for identity. A number of paradoxes seem to oppose this view; they are not jerry-rigged but seem to concern our constant, everyday experience. I will focus on the problem of change, as exemplified by the argument from temporary intrinsics. There are two kinds of solutions to this problem, which concern the nature of objects’ persistence through time. We will spend most of our time on David Lewis’ account of persistence, which is founded on the notion of temporal parts, and the “rotating disk” line of thinking against it, due to Saul Kripke and David Armstrong.