This unique book presents a comprehensive and rigorous treatment of the theory of computability which is introductory yet self-contained. It takes a novel approach by looking at the subject using computation models rather than a limitation orientation, and is the first book of its kind to include software. Accompanying software simulations of almost all computational models are available for use in conjunction with the text, and numerous examples are provided on disk in a user-friendly format. Its applications to computer science itself include interesting links to programming language theory, compiler design theory, and algorithm design. The software, numerous examples, and solutions make this book ideal for self-study by computer scientists and mathematicians alike.