Hi - I hope to see some of you in Marseille for Geocal06! I'll be talking about "universal algebra and diagrammatic reasoning", and there's a bunch of lecture notes here: http://math.ucr.edu/home/baez/universal/ Abstract: Since the introduction of category theory, the old subject of "universal algebra" has diversified into a large collection of frameworks for describing algebraic structures. These include "monads" (formerly known as "triples"), the "algebraic theories" of Lawvere, and the "PROPs" of Boardman and Vogt. We give an overview of these different frameworks, which are closely related, and explain how one can reason diagrammatically about algebraic structures defined using them. We focus on the bar construction and the relation between algebraic theories and PROPs. (I feel guilty for not talking about operads... I'll do it if there's time!) Best, jb