CONTENTS § 1. Introduction § 2. Reduction theorems § 3. The abstract version of Problems A and B with cost function satisfying the triangle inequality § 4. Proofs of the main theorems. Discussion of Theorem 1.1 and its generalization to non-metrizable compact spaces § 5. The problem of mass transfer and a mass statement of the duality problem § 6. Extension theorems and one problem on continuous selectors References