The aim of this textbook is to provide undergraduate students with an introduction to the basic theoretical models of computability, and to develop some of the model's rich and varied structure. 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. The first part of the book is devoted to finite automata and their properties. Then, material on pushdown automata provides a broader class of models and enables the analysis of context-free languages. In the remaining chapters, Turing machines are introduced and the book culminates in discussions of effective computability, decidability, and Gödel's incompleteness theorems. Plenty of exercises are provided, ranging from the easy to the challenging. As a result, this text will make an ideal first course for students of computer science.