I'll provide an overview of (1) hyperplane arrangements (2) counting points on hyperplane arrangements (3) Rota's conjecture and the idea of Huh's proof of Rota's conjecture (4) the connections to tropical geometry and (5) the recent idea of the "Chow ring of a matroid". The point is to motivate you to be interested in these concepts, which we'll be exploring throughout the term; many ideas will just be sketched.