What are the "correct" references for the Vassiliev invariant? Is there a good survey paper which describes the general ideas of
Vassiliev's invariant? I am not an expert on knot theory, many references are too technical for me.
Could Vassiliev's invariants be defined for general embeddings (rather than knot theory)? What are the useful references?
Thanks.
 A: A short introduction to some ideas of this theory is Kontsevich, M. (1993). Vassiliev's Knot Invariants. Advances in Soviet Mathematics. Vol 16, Part 2. I think that also the following two papers give a general idea of Vassiliev's invariants: Bar-Natan, D. Finite Type Invariants (this is an overview written for the Encyclopedia of Mathematical Physics), Bar-Natan, D. (1995). The fundamental Theorem of Vasilliev's Invariants. Lecture Notes.
If you are interested in a good introduction to these invariants which is written for readers with little background in knot theory, I'd suggest you Chmutov, S., Duzhin, S., & Mostovoy, J. (2012). Introduction to Vassiliev Knot Invariants. Cambridge: Cambridge University Press. Here, some technical results are not entirely proven (they instead refer to other papers for the details); moreover, the book also deals with more advanced topics, so I think that this is a really good reference.
A: Along with the references provided already, I think many people like New points of view in knot theory by Joan Birman. She gives a good explanation of the connections between these finite type invariants and knot polynomials.
