Derivation of additive functions of a set and of an interval § 1. Introduction § 2. Derivates of functions of a set and of an interval § 3. Vitali's Covering Theorem § 4. Theorems on measurability of derivates § 5. Lebesgue's Theorem § 6. Derivation of the indefinite integral § 7. The Lebesgue decomposition § 8. Rectifiable curves § 9. De la Vallée Poussin's theorem § 10. Points of density for a set § 11. Ward's theorems on derivation of additive functions of an interval § 12. A theorem of Hardy-Littlewood § 13. Strong derivation of the indefinite integral § 14. Symmetrical derivates § 15. Derivation in abstract spaces § 16. Torus space