Abstract: I am planning to give a series of talks about my work (three papers; JPAA, 1997) "Generalized sketches as a framework for completeness theorems", and some of the, mostly unpublished, work continuing the papers. After presenting the basic part of the theory of the 1997 papers, I will talk about the syntactic aspects of the system in more detail. A proposed efficient computer-aided processing of the syntax uses relational databases. There is a possibility of parallel processing essentially free of conflict constraints. I find it important to make detailed comparisons with traditional logical syntax. On later occasions, I will indicate how generalized sketches are used for a "plus-one dimensional" generalization ("categorification") of the fundamental Gabriel-Ulmer theory of essentially algebraic categories; now, we will have essentially algebraic 2-categories.