- Complex numbers, open sets in the plane.
- Continuity of functions of a complex variable
- Derivative at a point and Cauchy–Riemann equations
- Analytic functions; example of power series and elementary functions
- Cauchy’s theorem and applications.
- Cauchy’s formula and power series expansions
- Morera’s theorem
- Existence of a logarithm and of a square root
- Liouville’s theorem and the fundamental theorem of algebra
- Laurent series and classification of isolated singular points. The residue theorem
- Harmonic functions
- Schwarz’ lemma and applications
- Some ideas on conformal mappings
- Computations of integrals