Abstract: "Lecture 1" is meant as the talk I gave at the Grothendieck meeting recently held at the UdeM. "Lecture 2" is the one I am giving on March 3rd in this seminar. In Lecture 3, I will expand the scope of the theme of "pretopos" and conceptual completeness from finitary logic to infinitary logic. The main source is still MM/G.E. Reyes: "First order categorical logic", Springer LNM 611 (1977). The logic is L-infinity-omega: infinitary propositional connectives, single-variable quantifiers. The monograph "First order categorical logic" is about the relating L-infinity-omega to Grothendieck topos theory. There will be notes posted for all of the lectures.