  Let $(X,g)$ be a compact Riemannian stratified space with simple edge
singularity. Thus a neighbourhood of the singular stratum is a bundle of
truncated cones over a lower dimensional compact smooth manifold. We calculate
the various polynomially weighted de Rham cohomology spaces of $X$, as well as
the associated spaces of harmonic forms. In the unweighted case, this is
closely related to recent work of Cheeger and Dai \cite{CD}. Because the metric
$g$ is incomplete, this requires a consideration of the various choices of
ideal boundary conditions at the singular set. We also calculate the space of
$L^2$ harmonic forms for any complete edge metric on the regular part of $X$.
