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.