Finite type invariants of knots or links can be defined combinatorially using only link projections in S. In this setting it can be seen that every Jones-type polynomial invariant (quantum invariants) is equivalent to a sequence of finite type invariants. See [B2, BN] and references therein. Although Vassiliev’s original approach to finite type knot invariants ([V]) rests on topological foundat...

This is an overview article on finite type invariants, written for the Encyclopedia of Mathematical Physics.