Analytic Philosophy is a rich and diverse philosophical tradition that grew up around developments in the philosophy of logic and the philosophy of language in the early 20th century. It continues to grow and develop today. One can get to know this tradition in a variety of ways: for example, by studying its history or by surveying the topics on which analytic philosophers have focused. We are going to do something a little different: we are going to develop an understanding of Analytic Philosophy by focusing on a particular phenomenon that occurs throughout the history of philosophy (from the very get-go, in fact): the paradox. Roughly speaking, a paradox occurs when apparently good reasoning from innocent starting points leads us into an obvious falsehood. Paradoxes played a particularly important and constructive role in Analytic Philosophy. They are complicit in two of the most significant developments in logic and mathematics in the twentieth century; they are a common thread binding Analytic Philosophy to the larger corpus of philosophical thought; many of them remain unsolved; they are at once fascinating and infuriating!