Computability is concerned with the question of what computers can do in principle. Since Enderton directly contributed to the very areas that this book covers (computability and computational complexity), he is able to provide a concise and comprehensive firsthand view of the subject. As a scholar in the field, as well as in the history of logic, he frequently includes historical passages when presenting new concepts in the book.

Enderton starts with an unusual topic: decidable sets; this is an excellent point of departure to start talking about calculability. He creatively uses “digression” and “informal” discussion sections, providing readers with a context and a critical framework.

The book covers relative computability, structures such as the arithmetical hierarchy, and connections to logic such as the concept of forcing. It ends with two very interesting chapters on degrees of unsolvability and time complexity theory. The book’s unusual breadth of coverage and inclusion of advanced topics can’t be found elsewhere in the literature at this level.

This is a beautifully written and beautifully printed book, though the price may be a bit high considering its length (not even 200 pages). Also, there are some mistakes, particularly in the example sections at the end of each chapter.

The book would work perfectly as a textbook, covering standard material for one- or two-semester courses in computability or recursion theory. It is also an excellent study guide and reference for students and researchers in related areas. It is a lovely, short book that contains great ideas.