I think Raemon has a good overview of everything here:
In addition, MIRI has a recommended textbooks list
Also, CHAI has a textbooks list here
Also, Toon Alfrink has started RAISE to help bring people up to speed.
(META: I think this topic has a very long history of already being discussed. See, for example, lukeprog on the best textbooks. Also, we've tried having monthly open-thread-like-discussion-things in the past, and they sort of flopped. So just a heads-up if you're aiming for something similar.)
[CKC]: I intend this to be a Community Knowledge Convergence project - that is to say, I do not think I am particularly well informed on the subject, and I think there's a lot to be gained from compiling an understanding of what others in the LessWrong community consider as very important, probably important, possibly important, or maybe important.
What academic subjects do you consider most important to the study of AI safety? What non-academic subjects would you recommend?
Currently, here are the subjects I think are most important.
You might be able to tell, I'm not very well versed in this discipline. Please comment and add more subjects for me to add to the [June 2018] posts.