  In this paper we develop a theory for constructing an invariant of closed
oriented 3-manifolds, given a certain type of Hopf algebra. Examples are given
by a quantised enveloping algebra of a semisimple Lie algebra, or by a
semisimple involutory Hopf algebra. The invariant is defined by a state sum
model on a triangulation. In some cases, the invariant is the partition
function of a topological quantum field theory.
