ONTIC, the interactive system for verifying "natural" mathematical arguments that David McAllester describes in this book, represents a significant change of direction in the field of mechanical deduction, a key area in computer science and artificial intelligence. ONTIC is an interactive theorem prover based on novel forward chaining inference techniques. It is an important advance over such earlier systems for checking mathematical arguments as Automath, Nuprl, and the Boyer Moore system. The first half of the book provides a high-level description of the ONTIC system and compares it with these and other automated theorem proving and verification systems. The second half presents a complete formal specification of the inference mechanisms used. McAllester's is the only semi automated verification system based on classical Zermelo-Fraenkel set theory. It uses object oriented inference, a unique automated inference mechanism for a syntactic variant of first order predicate calculus. The book shows how the ONTIC system can be used to check such serious proofs as the proof of the Stone representation theorem without expanding them to excessive detail.