  We give a construction of the abelian Chern-Simons gauge theory from the
point of view of a 2+1 dimensional topological quantum field theory. The
definition of the quantum theory relies on geometric quantization ideas which
have been previously explored in connection to the nonabelian Chern-Simons
theory [JW,ADW]. We formulate the topological quantum field theory in terms of
the category of extended 2- and 3-manifolds introduced by Walker [Wa] and prove
that it satisfies the axioms of unitary topological quantum field theories
formulated by Atiyah [A1].
