  We introduce a new invariant of tangles along with an algebraic framework in
which to understand it. We claim that the invariant contains the classical
Alexander polynomial of knots and its multivariable extension to links. We
argue that of the computationally efficient members of the family of Alexander
invariants, it is the most meaningful.
  These are lecture notes for talks given by the first author, written and
completed by the second. The talks, with handouts and videos, are available at
http://www.math.toronto.edu/drorbn/Talks/Regina-1206/. See also further
comments at http://www.math.toronto.edu/drorbn/Talks/Caen-1206/#June8.
