  The theory of finitely generated relative (co)tilting modules has been
established in the 1980s by Auslander and Solberg, and infinitely generated
relative tilting modules have recently been studied by many authors in the
context of Gorenstein homological algebra. In this work, we build on the theory
of infinitely generated Gorenstein tilting modules by developing "Gorenstein
tilting approximations" and employing these approximations to study Gorenstein
tilting classes and their associated relative cotorsion pairs. As applications
of our results, we discuss the problem of existence of complements to partial
Gorenstein tilting modules as well as some connections between Gorenstein
tilting modules and finitistic dimension conjectures.
