In Mathematics of the Transcendental, Alain Badiou painstakingly works through the pertinent aspects of category theory, demonstrating their internal logic and veracity, their derivation and distinction from set theory, and the ’thinking of being’. In doing so he sets out the basic onto-logical requirements of his greater and transcendental logics as articulated in his magnum opus, Logics of Worlds. Previously unpublished in either French or English, Mathematics of the Transcendental provides Badiou’s readers with a much-needed complete elaboration of his understanding and use of category theory. The book is vital to understanding the mathematical and logical basis of his theory of appearing as elaborated in Logics of Worlds and other works and is essential reading for his many followers.