Introduction to the theory of computability: Turing machines and other models of computation, Church’s thesis, computable and noncomputable functions, recursive and recursively enumerable sets, many-one reductions. Introduction to complexity theory: P, NP, polynomial time reducibility, NP-completeness, self-reducibility, space complexity (L, NL, PSPACE and completeness for those classes), hierarchy theorems, and provably intractable problems.