I collected the following "top eight" text books on computability (in alphabetical order):

  • Boolos et al., Computability and Logic

  • Cooper, Computability Theory

  • Davis, Computability and unsolvability

  • Hermes, Enumerability, decidability, computability

  • Hopcroft et al., Introduction to Automata Theory, Languages, and Computation
    (thanks to Bill Province)

  • Kleene, Introduction to Metamathematics

  • Minsky, Computation

  • Sipser, Introduction to the Theory of Computation
    (thanks to Prajwal Kansakar)

I know it's opinion-based, but which important text books did I miss?


Cutland, Computability (CUP). A beautifully lucid and elegant classic text.


I'd say that [Odifreddi 1989] is still a good text to have, to use it at least as a reference book (but pretty good as a textbook too, I found).

One can also take a look at Peter Smith's "Teach yourself logic guide", where different sources are cited and commented upon. It covers much more than just computability, though there's a section exclusively on it (edit: now that I checked it again, there are actually two sections: 5.3 and 7.3 in the current version).