S.Chmutov, S.Duzhin.

The Kontsevich integral.

This is an expository paper whose purpose is to explain the famous
contribution of Maxim Kontsevich to Vassiliev knot invariant theory. More
specifically, our aim is to present a proof of Kontsevich's fundamental
theorem, which states that for each weight system there exists a Vassiliev
invariant whose symbol is exactly the given weight system, or, in other
words, that the only relations in the graded algebra of Vassiliev knot
invariants are the 1- and 4-term relations.
We also discuss the behaviour of the Kontsevich integral with respect
to mirror reflection, change of orientation and mutations.