We introduce a family of rank functions and related notions of total
transcendence for Galois types in abstract elementary classes. We focus, in
particular, on abstract elementary classes satisfying the condition know as
tameness (currently suspected to be a necessary condition for the development
of a reasonable classification theory) where the connections between stability
and total transcendence are most evident. As a byproduct, we obtain a partial
upward stability transfer result for tame abstract elementary classes stable in
a cardinal lambda satisfying lambda^{aleph_0}, a substantial generalization of
a result of Baldwin, Kueker, and VanDieren.