  This is a (slightly edited) version of the PhD dissertation of the author,
submitted to Brown University in July 2005.
  We construct a homotopy calculus of functors in the sense of Goodwillie for
the categories of rational homotopy theory. More precisely, given a homotopy
functor between any of the categories of differential graded vector spaces
(DG), reduced differential graded vector spaces, differential graded Lie
algebras (DGL), and differential graded coalgebras (DGC), we show that there is
an associated approximating "rational Taylor tower" of excisive functors. The
fibers in this tower are homogeneous functors which factor as homogeneous
endomorphisms of the category of differential graded vector spaces.
Furthermore, we develop very straightforward and simple models for all of the
objects in this tower. Constructing these models entails first building very
simple models for homotopy pushouts and pullbacks in the categories DG, DGL,
and DGC. We end with a short example of the usefulness of our computationally
simple models for rational Taylor towers, as well as a preview of some further
results dealing with the structure of rational (and non-rational) Taylor
towers.
