A challenging puzzle collection and an instructive and entertaining introduction to Kurt Godel's famous theorems, including incompleteness and undecidability. Much of the action of the book takes place on an imaginary and magical island, the Island of Knights and Knaves, where knights always make true statements, knaves always make false statements, and every inhabitant is either a knight or a knave. Here we meet an amazing array of characters, visitors to the island, seeking to determine the natives' true identities. Among them are the census-taker McGregor; a philosopher-logician in search of his flighty bird-wife Oona; and a regiment of Reasoners. By following the Reasoners through brain-tingling exercises and adventures - including journeys into the "other possible worlds" of Kripke semantics - even the most illogical of us should come to understand Godel's theorems, some of their philosophical and mathematical implications and why we, like Godel himself, must remain forever undecided! The book is intended for puzzle fans of every age and ability - from the high-school whizz to the seasoned mathematician, logician or computer scientist.