Continues MATH 7314. Examines affine and projective schemes, their categories of quasi-coherent sheaves, and various classes of morphisms between schemes. Integrates general theory with examples from complex algebraic and arithmetic geometry. Covers reduced and integral schemes, normal and factorial schemes, coherent sheaves, morphisms of schemes and their images, finite morphisms, Cartier divisors, regular sequences, open and (locally) closed embeddings, fiber products of schemes, and base change.