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
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