ELEMENTARY GEOMETRICAL METHODS OF THE THEORY OF FUNCTIONS § 1. Translation of poles § 2. Runge's theorem. Cauchy's theorem for a simply connected region § 3. Branch of the logarithm § 4. Jensen's formula § 5. Increments of the logarithm and argument along a curve § 6. Index of a point with respect to a curve § 7. Theorem on residues § 8. The method of residues in the evaluation of definite integrals § 9. Cauchy's theorem and formula for an annulus § 10. Analytical definition of a simply connected region § 11. Jordan's theorem for a closed polygon § 12. Analytical definition of the degree of connectivity of a regio