Abstract: The weak and strong Lefschetz properties are connected to many topics in algebraic geometry, commutative algebra and combinatorics. Some of these connections are quite surprising and there are still several open questions. The goal of this talk is to introduce weak and strong Lefschetz properties, and the related notion of almost revlex ideal, in the non-Artinian case, and then apply the obtained results to the study of the Jacobian algebra of a hyperplane arrangement.