  Let $S$ be a closed, oriented surface with a finite (possibly empty) set of
points removed. In this paper we relate two important but disparate topics in
the study of the moduli space $\M(S)$ of Riemann surfaces: Teichm\"{u}ller
geometry and the Deligne-Mumford compactification. We reconstruct the
Deligne-Mumford compactification (as a metric stratified space) purely from the
intrinsic metric geometry of $\M(S)$ endowed with the Teichm\"{u}ller metric.
We do this by first classifying (globally) geodesic rays in $\M(S)$ and
determining precisely how pairs of rays asymptote. We construct an "iterated
EDM ray space" functor, which is defined on a quite general class of metric
spaces. We then prove that this functor applied to $\M(S)$ produces the
Deligne-Mumford compactification.
