TOPICS IN ALGEBRAIC TOPOLOGY I: KNOT THEORY, LIE ALBEBRAS, AND LIE BI-ALGEBRAS. After some preliminaries and warm up examples from knot theory I will describe how the theory of finite type invariants of knots fully explains why there is a knot invariant for each Lie algebra and representation thereof, how it nearly (but doesn't quite) explains the polynomiality and computability of these invariants, and how it completely fails to create a context to the fact that these invariants can be categorified. Much work remains!