The integral in an abstract space § 1. Introduction § 2. Terminology and notation § 3. Abstract space X § 4. Additive classes of sets § 5. Additive functions of a set § 6. The variations of an additive function § 7. Measurable functions § 8. Elementary operations on measurable functions § 9. Measure § 10. Integral § 11. Fundamental properties of the integral § 12. Integration of sequences of functions § 13. Absolutely continuous additive functions of a set § 14. The Lebesgue decomposition of an additive function § 15. Change of measure