  We define several homology theories for central hyperplane arrangements,
categorifying well-known polynomial invariants including the characteristic
polynomial, Poincare polynomial, and Tutte polynomial. We consider basic
algebraic properties of such chain complexes, including long-exact sequences
associated to deletion-restriction triples and dg-algebra structures. We also
consider signed hyperplane arrangements, and generalize the odd Khovanov
homology of Ozsvath-Rasmussen-Szabo from link projections to signed
arrangements. We define hyperplane Reidemeister moves which generalize the
usual Reidemeister moves from framed link projections to signed arrangements,
and prove that the chain homotopy type associated to a signed arrangement is
invariant under hyperplane Reidemeister moves.
