Alain Badiou is one of the most important and widely discussed philosophers of our time. His main work "Being and Event," published in 1988, which gathers the fundamental aspects of his philosophy, is presented here in a revised second edition. It posits the radical thesis that since its Greek origins, it is mathematics—and only mathematics—that unfolds the process of thought concerning being. Nevertheless, there remains a place for what is not being: that of the event. The event is an excess term of transgression, beyond which knowledge cannot decide; a concept whose truth is never recognizable in advance. The subject is thus no longer a guarantor or support of truth, but rather a local, improbable instance that derives its little being from the aleatory emergence of a truth in the event.