Olaf has already given most of the references I would recommend. But in the case of Chern-Simons theories and knot theory, there are two (plus one) other very nice references. These are all written by physicist to physicists, so no modular functors, Cobordisms and so on.
1) Marcos Marino - Chern-Simons Theory and Topological Strings (arXiv:hep-th/0406005v4) Section II has a very good review of Chern-Simons theory and its relation to Knot invariants (and Rational CFT's).
2) Michio Kaku - String, Conformal Fields and M-Theory Don't be too scared by the title. Chapter 8 contain a very readable review of Chern-Simons theories and knot invariants. It introduces everything starting from a simple and intuitive starting point. For example shows how the abelian $U(1)$ Chern-Simons theory leads to the Gauss linking numbers by direct integration, and why one has to regularize with framing due to problem with self-linking. Chapter 12 is more generally about topological field theories, it discusses Cohomological Field theories, Floer theory, relations to Morse theory and so on. You might find this chapter a little more challenging than chapter 8.
3) Birmingham et al - Topological Field Theory This is a long, and a little old, review of many different topological field theories. It also contains a little bit about Chern-Simons theory but not as much as the other two above, as I remember.
I know many other good references, but they are more advanced. This is an advanced topic so most papers and books will naturally assume a certain background.
This post imported from StackExchange Physics at 2014-04-04 16:23 (UCT), posted by SE-user Heidar