This textbook provides undergraduate students with an introduction to the basic theoretical models of computability and develops some of the model s rich and varied structure. The first part of the book is devoted to finite automata and their properties. Pushdown automata provide a broader class of models and enable the analysis of context-free languages. In the remaining chapters Turing machines are introduced and the book culminates in analyses of effective computability decidability and Gödel s incompleteness theorems. Students who already have some experience with elementary discrete mathematics will find this a well-paced first course and a number of supplementary chapters introduce more advanced concepts.