The main purpose of my research is to study fundamental combinatorial, algebraic and topological properties of hyperplane arrangements and their applications. One of the main goals in my study of arrangements is to decide if a given invariant is determined by the combinatorics of the arrangement, and, if so, to express it explicitly in terms of the associated matroid, i.e the intersection lattice of the arrangement. In particular, I am interested in the class of free hyperplane arrangements, in the algebraic properties of the Jacobian algebra and the connection between arrangements and graph theory. Moreover, I am interested in the application of this theory, for example to economics, social choice theory, robotics, graphics, databases and cyber security.