  We review the concept of $\tau$-function for simple analytic curves. The
$\tau$-function gives a formal solution to the 2D inverse potential problem and
appears as the $\tau$-function of the integrable hierarchy which describes
conformal maps of simply-connected domains bounded by analytic curves to the
unit disk. The $\tau$-function also emerges in the context of topological
gravity and enjoys an interpretation as a large $N$ limit of the normal matrix
model.
