An Introduction to Khovanov Homology
  This paper is an introduction to Khovanov homology, starting with the Kauffman bracket state summation, emphasizing the Bar-Natan Canopoloy and tangle cobordism approach. The paper discusses a simplicial approach to Khovanov homology and a quantum model for it so that the graded Euler characteristic that produces the Jones polynomial from Khovanov homology becomes the trace of a unitary transformation on a Hilbert space associated with the Khovanov Homology. 
Louis H. Kauffman
math.GT