Abstract: The Jacobian ideal of a hyperplane arrangement is an ideal in the polynomial ring whose generators are the partial derivatives of the arrangements defining polynomial. In this talk, we will investigate various properties of this ideal. In particular, we prove that an arrangement can be reconstructed from its Jacobian ideal. We will first start with a elementary problem concerning lines and points in the plane, investigate the Jacobian ideal, and finally, if times permits, we will discuss an application to the study of punctual Hilbert schemes.