For about fifteen years, Alain Badiou worked on "Logics of Worlds," the continuation of his major work "Being and Event" (published in 1988, with diaphanes in 2005). But what does continuation mean? In 1988, the ontological concern was to demonstrate, based on mathematics, that being, as such, is merely indifferent multiplicity. The following problem then arises: How is it to be understood, against the backdrop of this indifference, that there are not only truths but that they also appear in certain worlds? What is the visible or objective body of a truth? This cannot be derived from ontology. Rather, a logic of appearance, a phenomenology, must be constructed. This is precisely the aim of the present book: a "Great Logic" that, by accounting for the order of worlds, engages with the thinking of truths.