Title: Khovanov homology of knots.

Abstract.

This is an introduction to the Khovanov homology of knots which catgorify 
the famous Jones polynomial. I introduce the Jones polynomial via the Kauffman 
bracket and then show how this definition can be converted into a construction 
of the Khovanov chain complex. The chain complex does depend on the knot 
diagram but its homology does not. I will give a simplest example of the 
calculation of the Khovanov homology and explain the idea of the proof of its 
invariance under the Reidemeister moves. 

A standard course of linear algebra 
should be sufficient for understanding most of the lecture. Although a familiarity 
with tensor product of vector spaces and abstract algebra would make it easier.