  We propose a notion of minimal free resolutions for differential modules, and
we prove existence and uniqueness results for such resolutions. We also take
the first steps toward studying the structure of minimal free resolutions of
differential modules. Our main result in this direction explains a sense in
which the minimal free resolution of a differential module is a deformation of
the minimal free resolution of its homology; this leads to structural results
that mirror classical theorems about minimal free resolutions of modules.
