I will give an overview of the contents of a future topics course in algebra and combinatorics. One goal is to extend several aspects of the classical theory of the free Lie algebra to a new theory relative to a hyperplane arrangement. For this, one needs to study various algebraic, geometric and combinatorial aspects of hyperplane arrangements. I will go over a few features of the classical case and suggest the proposed generalizations. Time permitting, I will indicate how the notion of Hopf algebra can be extended to the setting of hyperplane arrangements.

Basic knowledge of ring theory and of the combinatorics of hyperplane arrangements will be useful, although I will attempt to cover most of the prerequisites.