Content: A lattice is a partially ordered set in which every two elements a, b have a least upper bound a ∨ b and a greatest lower bound a ∧ b; equivalently, a set with with operations ∨ and ∧ satisfying appropriate identities. Examples include the lattice of all subgroups of any group, and obvious analogs with "group" replaced by "set", "ring", "lattice", etc.; the lattice of all convex subsets of a real vector space, and the lattice of all closed subsets of a topological space. (No relation to regular arrays of points in Euclidean space, also called "lattices".) As with groups, rings, etc., the structure theory of lattices is also studied in the abstract.
George Grätzer has asked for volunteers to read his draft of vol. 1 of a third edition of his book General Lattice Theory, and send him corrections and suggestions. I would like to do this as a seminar, in which we read a certain number of pages each week, meet and discuss the material, and give him feedback. I would write up and e-mail him our observations week by week. I held such a seminar in Fall 1999 for P. M. Cohn's Free ideal rings ..., which worked well. In the above seminar title, "can read" means "can comfortably read": we'll move forward week by week, ending wherever we find ourselves at the end of the Semester.
To my knowledge, none of our regular faculty specializes in the area; however, there have been occasional Berkeley theses on lattices (several under logicians and one under me), and we have an ongoing visitor who has done important work in the field, Dana Scott. In any case, lattice theory is a useful topic to have under one's belt, if one works in algebra or logic, or, to varying degrees, other fields. No familiarity with the subject will be assumed -- the text is self-contained.
Strong undergrads, grad students, faculty, and visitors are all welcome to participate. Students may either enroll or audit; if you enroll, please use the grading option Pass/Not-Pass (for undergrads) or Satisfactory/Unsatisfactory (for grads). If for some reason you want to enroll for a letter grade, discuss this with me.
Note: Another presentation of the topics of partially ordered sets (more extensive than that of Grätzer, and including a sketch of the axioms of set theory) and lattices (much briefer than Grätzer, of course) can be found in chapters 4 and 5 respectively of my Math 245 course notes.
Further notes
I've put online some suggested additional exercises that I've sent to Grätzer.