This title presents a range of critical engagements with the work of Alain Badiou. This collection of 13 essays directly addresses the work of Alain Badiou, focusing specifically on the philosophical content of his work and the various connections he established with both his contemporaries and his philosophical heritage. This is the first reassessment of Badiou's work since the publication of the English translation of Logics of Worlds, (2009). It critiques how Badiou sources and responds to existing philosophical arguments and traditions as well as the arguments he employs to do so. It examines Badiou's work through the lens of a number of thinkers and themes, from Cantor and category/topos theory, through Lacan and Lautman, to Sartre and subject.