The paper reviews the development of Chern-Simons gauge theory and its relation to knot and link invariants. The main focus is on the relation between perturbative Chern-Simons theory and Vassiliev finite type invariants. A table relating the knot theory concepts with the quantum field theory ones, which appeared in the author’s previous paper [Chern-Simons Gauge Theory: Ten Years After, Trends in Theoretical Physics II, AIP Conf. Proc. 484, 1-40 (1999)], is reproduced, and the discussion is guided by this table. In particular, there are three known types of gauge fixing, namely the Landau gauge, the light-cone gauge, and the temporal gauge, which produce three different expressions of perturbative Chern-Simons theory. The counterparts in knot theory of the first two of the three are the configuration space integral and the Kontsevich integral, respectively. It is an open question what construction in knot theory corresponds to the temporal gauge.
For the entire collection see [Zbl 0972.00032].