Donald Barthelme's 81 essential books for a literary education

Donald Barthelme ('31-'89) was a masterful short story writer. Despite never teaching a literature course nor receiving a degree, he left behind a list of what he considered required reading for anyone in the field of wording, coffee stains, and marginalia included. I have no clue about the two red check marks.
Barthelme's essential books, part 1
Barthelme's essential books, part 2
Barthelme's essential books, part 3