The final version of these notes has been published by American Math. Society; you can by it directly from them here for $29. Unfortunately, our contract with AMS prevents us from posting the final version on-line. What follows is the preliminary version (as of May 2000), which is actually rather close but not identical to the final version.
If you are interested in this subject, we also highly recommend a manuscript "On Witten's 3-manifold invariants" by Kevin Walker. This manuscript was written in 1991 and never finished or published. It is now available on-line at http://canyon23.net/math/.
These lectures are devoted to the discussion of the relation between tensor categories, modular functor, and 3D topological quantum field thery. They were written as a textbook; all the results there are known. Our only contribution is putting it all together, filling the gaps, and simplifying some arguments.
This is a preliminary version; it may contain some errors or inaccuracies (in fact, we know of some of them and are working on them) -- use at your own risk! If you have any comments or suggestions, we'd very much like to hear them; you can write to us at bakalov@math.mit.edu or kirillov@math.sunysb.edu.
The whole text is about 200 pages long and contains number of figures; it is posted as a collection of compressed (gzip'ed) PostScript files. If you are on a Unix or Linux machine, Netscape (or whatever browser you use) usually knows how to decompress them and starts the viewer program (Ghostview), so all you have to do is to click on the link below. Here they are: