Combinatorics of Vassiliev invariants

This paper is an introductory survey of the combinatorial aspects of the Vassiliev theory of knot invariants following the lectures delivered at the Advanced School on Knot Theory and its Applications to Physics and Biology in the ICTP, Trieste (Italy), May 2009. The exposition is based on the forth- coming book [CDM], where the reader may find further details, examples, and developments