  We compute some Gromov-Witten invariants of the moduli space of odd degree
rank two stable vector bundles over a Riemann surface of any genus. Next we
find the first correction term for the quantum product of this moduli space and
hence get the two leading terms of the relations satisfied by the natural
generators of its quantum cohomology. Finally, we use this information to get a
full description of the quantum cohomology of the moduli space when the genus
of the Riemann surface is 3.
