We started out by going over the notions of NP, polynomial-time reductions, and NP-Completeness. We carefully described the meaning of a problem being NP-Complete.
We described various NP-complete problems. All together, the problems covered were HAM-CYCLE, HAM-PATH, LONGEST-PATH, CIRCUIT-SAT, SAT, 3SAT, CLIQUE, SUBSET-SUM. For each we talked about membership in NP, but why membership in P seemed doubtful. In the case of SUBSET-SUM, this took us to a discussion of how to measure the size of a problem. We diagrammed what is reduced to what in the book, but we didn't do any actual reductions.