  It is a long-standing question to extend the definition of 3-dimensional
Chern-Simons theory to one which associates values to 1-manifolds with boundary
and to 0-manifolds. We provide a solution in case the gauge group is a torus.
We also develop from different points of view an associated 4-dimensional
invertible topological field theory which encodes the anomaly of Chern-Simons.
Finite gauge groups are also revisited, and we describe a theory of "finite
path integrals" as a general construction for a certain class of finite
topological field theories. Topological pure gauge theories in lower dimension
are presented as a warm-up.
