  This paper discusses the construction of a generalized Alexander polynomial
for virtual knots and links, and the reformulation of this invariant as a
quantum link invariant. The algebraic background for the generalized Alexander
module is formulated in terms of the biquandle, a generalization of the quandle
of David Joyce (which, in turn, is a generalization of the fundamental group of
the knot or link). We then introduce the concept of a bi-oriented quantum
algebra which provides an algebraic context for the associated quantum
invariant.
