Complex Analysis

1. Complex differentiability and the Cauchy‒Riemann equations
2. Contour integration
3. Cauchy's theorem and Cauchy's integral formula
4. Local theory of holomorphic functions
5. Elementary functions
6. The complex projective line and automorphisms of standard sets
7. The invariant metric of the unit disk
8. Extremum principles, open mapping theorem, Schwarz' lemma
9. Global theory of holomorphic functions
10. Meromorphic functions and the Riemann sphere
11. Complex-analytic methods for the computation of real integrals and series
12. Infinite products and factorisations
13. Elliptic functions
14. Modular forms
15. Dirichlet series and the Gamma function
16. Tauberian theorems
17. Analytic spaces and the ring of convergent power series
18. Julia sets and the Mandelbrot set
19. Bibliography