  In this thesis three topics on the model theory of partial differential
fields are considered: the generalized Galois theory for partial differential
fields, geometric axioms for the theory of partial differentially closed
fields, and the existence and properties of the model companion of the theory
of partial differential fields with an automorphism. The approach taken here to
these subjects is to relativize the algebro geometric notions of prolongation
and D-variety to differential notions with respect to a fixed differential
structure.
