  We introduce and study in detail an invariant of (1,1) tangles. This
invariant, derived from a family of four dimensional representations of the
quantum superalgebra U_q[gl(2|1)], will be referred to as the Links-Gould
invariant. We find that our invariant is distinct from the Jones, HOMFLY and
Kauffman polynomials (detecting chirality of some links where these invariants
fail), and that it does not distinguish mutants or inverses. The method of
evaluation is based on an abstract tensor state model for the invariant that is
quite useful for computation as well as theoretical exploration.
