  In these expository notes I discuss several concepts and results in the
theory of modules over commutative rings, revolving around the Gorenstein
dimension of modules. Some of the related notions are the Auslander dual,
k-torsionless modules, and k-th syzygies.
  Essentially everything in these notes can be found, in one form or another,
in the memoir "Stable module theory" by M. Auslander and M. Bridger (Mem.
A.M.S., no. 94, 1969). The only difference is in presentation. In the
Auslander-Bridger memoir many of the results are proved in the most general
setting, e.g. over possibly non-commutative, non-Noetherian rings. The
techniques used are quite abstract and unfamiliar to many commutative
algebraists. Much space is devoted to the theory of satellites of functors
which are exact only in the middle, etc. While such a degree of generality has
many advantages, it does make the memoir difficult to read for the non-expert.
My goal in writing these notes was to develop the theory in the context of
commutative Noetherian rings, and to show that, in this important special case,
the theory is fairly elementary and easy to build. As a practical matter, then,
I wrote the notes using Matsumura's "Commutative ring theory" as the only
pre-requisite; and indeed, my hope is that these notes can be read just like an
extra chapter in Matsumura's book.
