This is a list of computability and complexity topics, by Wikipedia page.

Computability theory is the part of the theory of computation that deals with what can be computed, in principle. Computational complexity theory deals with how hard computations are, in quantitative terms, both with upper bounds (algorithms whose complexity in the worst cases, as use of computing resources, can be estimated), and from below (proofs that no procedure to carry out some task can be very fast).

For more abstract foundational matters, see the list of mathematical logic topics. See also list of algorithms, list of algorithm general topics.