Topology of plane arrangements and their complements

This paper is a glossary of notions and methods related to the topological theory of affine plane arrangements, including braid groups, configuration spaces, order complexes, stratified Morse theory, simplicial resolutions, complexes of graphs, Orlik–Solomon rings, Salvetti complexes, matroids, Spanier–Whitehead duality, twisted homology groups, monodromy theory, and multidimensional hypergeometric functions. The emphasis is upon making the presentation as geometric as possible. Applications and analogies in differential topology are outlined, and some recent results of the theory are presented.