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. Global theory of holomorphic functions
9. Meromorphic functions and the Riemann sphere
10. Complex-analytic methods for the computation of real integrals and series
11. Infinite products and factorisations
12. Elliptic functions
13. Modular forms
14. Dirichlet series and the Gamma function
15. Tauberian theorems
16. Analytic spaces and the ring of convergent power series
17. Julia sets and the Mandelbrot set
18. Bibliography