THIS IS A JOINT TOPOLOGY/ALGEBRAIC TOPOLOGY SEMINAR.  Chas and Sullivan introduced in 1999 a product on the homology of the free loop space LM  of a compact, oriented manifold M.  I will discuss some related higher order string topology operations that are the result of joint work with Ralph Cohen and Nathalie Wahl.  Some are constructed using Morse's finite dimensional approximation of LM. Others are parameterized by Sullivan diagrams.