Alain Badiou's philosophical project is a genuine system in the traditional sense. It profoundly shakes up the field of thought as well as offering fresh insights into contemporary events. His concepts are becoming indispensable tools in a variety of fields, from philosophy to anthropology, including art, politics and theatre. From Antiphilosophy to Worlds and from Beckett to Wittgenstein, over 90 entries in this dictionary provide detailed explanations and engagements with his key concepts and some of his major interlocutors. They also reflect the crucial divergences in Badiou scholarship in a productive and enlightening way.