This course will be presented based on the knowledge of the Bachelor course "Elemente der Funktionentheorie". Besides reminding some basic results of complex analysis, we will cover the following topics:

• Riemann sphere and spherical distance.
• Partial complex differentiations, the complex Green-Gauss integral theorem and the general Cauchy integral theorem,
• Residue theorem and its applications,
• Conformal mappings, the Möbius transformations, Riemann's Mapping theorem,
• Construct holomorphic and meromorphic functions via Mittag-Leffler's theorem, Weierstrass factorization theorem.
• Special holomorphic and meromorphic functions: Gamma function, Riemann zeta function, elliptic functions.
• Harmonic functions, boundary value problems.