UofM: quantum groups and Jones polynomial
Links:
Selected Wikipedia biographies:
Teller (very interesting read, but much more physics than math).
Here is link to Weyl's book on Classical Groups
To learn more about classical groups and their representations start by looking at the book by Fulton and Harris "Representation Theory: A First Course".
Wikipedia on Reidemeister moves
Kuperberg's paper which generalizes R.T.W.'s diagrammatic description of $SL_2$ to $SL_3$, $Sp_4$ and $G_2$.