The concept of an analytic function General properties of rational functions Linear transformations Mapping by rational functions of second order The exponential function and its inverse. The general power The trigonometric functions Infinite series with complex terms Integration in the complex domain. Cauchy's theorem Cauchy's integral formula and its applications The residue theorem and its applications Harmonic functions Analytic continuation Entire functions Periodic functions The Euler $\Gamma$-function The Riemann $\zeta$-function The theory of conformal mapping Index.

The authors present topics usually treated in a complex analysis course, starting with basic notions (rational functions, linear transformations, analytic function), and culminating in the discussion of conformal mappings, including the Riemann mapping theorem and the Picard theorem