1. The Riemann Sphere: Circles. Functions. Meromorphic Functions. Rational Functions. Automorphisms. The Group PGL(2, C).
2. Periodic Functions: Simply Periodic Functions. Lattices and Fundamental Regions. Elliptic Functions. Congruence Classes of Zeros and Poles.
3. Continuations: Meromorphic Continuations. Analytic Continuations. Power series Continuations. Regular and Singular Points. Path Continuations. Sheaf and Germs.
4. Riemann Surfaces: Covering Maps. The Riemann Surface of the Logarithm. The Riemann Surface of the Cube Root Function. Abstract Riemann Surfaces. Functions. Covering Surfaces. Regular Covering Spaces.