Godel's modal ontological argument is the centerpiece of an extensive examination of intensional logic. First, classical type theory is presented semantically, tableau rules for it are introduced, and the Prawitz/Takahashi completeness proof is given. Then modal machinery is added to produce a modified version of Montague/Gallin intensional logic. Finally, various ontological proofs for the existence of God are discussed informally, and the Godel argument is fully formalized. Parts of the book are mathematical, parts philosophical.