Gamma-function. Stirling formula in the complex plane.

Riemann zeta-function: analytic continuation and functional
equation. Prime number theorem.

Elliptic functions.

Harmonic functions. Poisson-Jensen formula and its applications.

Entire and meromorphic functions. Theorems of Bloch and Picard.

Entire functions of finite order, Hadamard factorization theorem.

Biholomorphic mappings of plane domains. Riemann mapping theorem.
Boundary behaviour of conformal mappings.

Analytic functions of several variables. Hartogs-Osgood removable
singularity theorem.