Badiou, quite late in the day, in the wake of the fading giants of poststructuralism, has drawn from them and tried to revivify the philosophical enterprise.
I'm not entirely convinced that ontology is inscribed by mathematics and, set theory in particular - but it is a fascinating theoretical concept: that mathematical thought is the thought of being. Interestingly Badiou manages to link Parmenides to Being through Set Theory. Personally, I like the idea but think the mathematics Badious wants has yet to be created - still it is a bold step.
The idea that aside from Being there are Events which irrupt out of the void of Being, the uncounted, the glossed over, This again has tremendous intellectual force but Badiou, I think, succeeds in introducing the conception but I don't think his limited materialistic position does full justice and it will wait for a future philosopher to take this idea further and truly bring out its revolutionary forice.
All of this sounds negative but it isn't. Badiou is a much needed French counterpoint to the excesses of postmodernism and his return to Plato - again rather distorted and muddled - is worthy of thought.
In all honest you should read Heidegger's Being and Time and sidestep the deconstructionist tradition that has stolen him. Badiou is a good follow on from Heidegger in that respect.