Covers machine models and formal specifications of the classes of computational problems they can solve. The central concepts are the Turing machine and the classes of decidable and computably enumerable languages. The Halting Problem and other natural problems are shown to be undecidable by Turing machines, implying that they are undecidable by high-level programming languages or any other known computational model. Finite automata, which are Turing machines without external memory, are shown to correspond to the class of regular languages. The course also covers regular expressions, time and space complexity of Turing machines, reducibility between problems, and NP-completeness.