  This paper provides an overview of selected results and open problems in the
theory of hyperplane arrangements, with an emphasis on computations and
examples. We give an introduction to many of the essential tools used in the
area, such as Koszul and Lie algebra methods, homological techniques, and the
Bernstein-Gelfand-Gelfand correspondence, all illustrated with concrete
calculations. We also explore connections of arrangements to other areas, such
as De Concini-Procesi wonderful models, the Feichtner-Yuzvinsky algebra of an
atomic lattice, fatpoints and blowups of projective space, and plane curve
singularities.
