  It has been folklore for several years in the knot theory community that
certain integrals on configuration space, originally motivated by perturbation
theory for the Chern-Simons field theory, converge and yield knot invariants.
This was proposed independently by Gaudagnini, Martellini, and Mintchev and
Bar-Natan. The analytic difficulties involved in proving convergence and
invariance were reportedly worked out by Bar-Natan, Kontsevich, and Axelrod and
Singer.
  But I know of no elementary exposition of this fact. ... This thesis is an
attempt to remedy this lack. I adopt an almost exclusively topological point of
view, rarely mentioning Chern-Simons theory. There are also a few new results
in this thesis. These include a new construction of the functorial
compactification of configuration space (Section 3.2) as well as some
variations on the integrals. For a suitable choice of this variation, the
integral reduces to counting tinkertoy diagrams (Section 4.5). In particular,
the invariants constructed take values in Q.
