# Complex Analysis

- Complex differentiability and the Cauchy‒Riemann equations
- Contour integration
- Cauchy's theorem and Cauchy's integral formula
- Local theory of holomorphic functions
- Elementary functions
- The complex projective line and automorphisms of standard sets
- The invariant metric of the unit disk
- Extremum principles, open mapping theorem, Schwarz' lemma
- Global theory of holomorphic functions
- Meromorphic functions and the Riemann sphere
- Complex-analytic methods for the computation of real integrals and series
- Infinite products and factorisations
- Elliptic functions
- Modular forms
- Dirichlet series and the Gamma function
- Tauberian theorems
- Analytic spaces and the ring of convergent power series
- Julia sets and the Mandelbrot set
- Bibliography