Orlik–Solomon algebras in algebra and topology

This is a survey of Orlik–Solomon algebras of hyperplane arrangements. These algebras first appeared in theorems due to Arnol'd, Brieskorn, and Orlik and Solomon as the cohomology algebras of the complements of complex hyperplane arrangements. Numerous applications of these algebras have subsequently been found. This survey is confined to studying Orlik–Solomon algebras per se and some of their applications to topology and combinatorics. Most of the results are taken from recent papers and preprints, although for the reader's convenience we also include relevant definitions and basic facts from the book Arrangements of hyperplanes by Orlik and Terao. For some of these facts new and more straightforward or shorter proofs are given.