Slavoj Zizek is not alone in thinking that Alain Badiou's recent work is "the event of contemporary philosophy". Think Again, the first publication of its kind, goes a long way towards justifying his assessment. Badiou is nothing if not polemical and the most suitable way to approach his philosophy is precisely through the controversies it creates. Think Again, which opens with an introduction aimed at readers new to Badiou's work, presents a range of essays which explore Badiou's most contentious claims in the fields of ontology, politics, ethics and aesthetics. Alain Badiou has devised perhaps the only truly inventive philosophy of the subject since Sartre. Almost alone among his peers, Badiou's work promises a genuine renewal of Philosophy, a subject he sees as conditioned by innovation in spheres ranging from radical politics to artistic experimentation to mathematical formalisation.