Part I: The basics of finite type invariants. The definition and motivation for finite type invariants. The Conway polynomial is finite type. Chord diagrams, weight systems and universal invariants. Behavior under natural operations: strand deletion and doubling, etc. The relation with Lie algebras and the formal PBW theorem.

Part II: Algebraic construction of a universal finite type invariants. A brief discussion of the (so far failed) topological construction and the (successful but weird) analytical constructions. Systems of generators and relations for knot theory. The relation with the pentagon equation. The reduction to a cohomological problem.

I understand that I'm also going to give a shorter and more advanced talk earlier in the day. I plan it to be a quick description of the "Aarhus" construction of the LMO universal finite type invariant for integral/rational homology spheres. If you insist on a title, it will be "On Links, Functions, Integrals and 3-Manifold Invariants".

**Talk video** ("advanced talk" only):
and/or
@CUNY.