>>3
The syllabus says there's no textbook and seems to suggest that the lecture notes are enough. I've no idea how well that works for self-study, however. After some DDGing around it looks like there are some computability theory lectures available on Youtube and a number of textbooks, although nothing tailored specifically for this course. This one at least is edited in part by the professor of 6.844:
http://hjemmesider.diku.dk/~neil/comp2book2007/book-whole.pdf
Worth mentioning that in addition to the intro CS class the syllabus also mentions their discrete math class as a prerequisite, and OCW does have the full video lectures for that (with slides in glorious Comic Sans):
https://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-042j-mathematics-for-computer-science-spring-2015/