  Consideration of the Noether variational problem for any theory whose action
is invariant under global and/or local gauge transformations leads to three
distinct theorems. These include the familiar Noether theorem, but also two
equally important but much less well-known results. We present, in a general
form, all the main results relating to the Noether variational problem for
gauge theories, and we show the relationships between them. These results hold
for both Abelian and non-Abelian gauge theories.
