ANALYTIC FUNCTION § 1. Introductory remarks § 2. Analytic element § 3. Analytic continuation along a curve § 4. Analytic functions § 5. Inverse of an analytic function § 6. Analytic functions arbitrarily continuable in a region § 7. Theorem of Poincaré-Volterra § 8. An analytic function as an abstract space § 9. Analytic functions in an annular neighbourhood of a point § 10. Analytic functions in an annular neighbourhood as an abstract space § 11. Critical points § 12. Algebraic critical points § 13. Auxiliary theorems of algebra § 14. Functions with algebraic critical points § 15. Algebraic functions § 16. Riemann surfaces