This book continues Alain Badiou's project to posit an integral link between mathematics and ontology. Originally published as part of a trilogy in 1998, Briefings on Existence engages the ideas of Deleuze, Spinoza, Plato, Aristotle, and Kant and outlines how the philosophical inquiry into Being and existence converges with the possible world topology of category theory. Set against the background of a multiplication of gods that can be declared dead (the gods of religions, metaphysics, and poetry), Badiou argues that the extension of these events has fallen short of accomplishing its collective promise, but can be achieved through the mathematical understanding of ontology. After several remarkable decades of theoretical invention, French philosophy stands at a crossroads, and Badiou's egalitarian materialism is one of its strongest calls forward.