1. Preliminaries: Set Theory and Topology. - 2. Preliminaries: Vector Spaces and Complex Variables. - 3. Properties of C(G) and H(G). - 4. More About C(G) and H(G). - 5. Duality. - 6. Duality of H(G) The Case of the Unit Disc. - 7. The Hahn-Banach Theorem and Applications. - 8. More Applications. - 9. The Dual of H(G). - 10. Runge's Theorem. - 11. The Cauchy Theorem. - 12. Constructive Function Theory. - 13. Ideals in H(G). - 14. The Riemann Mapping Theorem. - 15. Carathéodory Kernels and Farrell's Theorem. - 16. Ring (not Algebra) Isomorphisms of H(G). - 17. Dual Space Topologies. - 18. Interpolation. - 19. Gap-Interpolation Theorems. - 20. First-Order Conformal Invariants. - References. Language: English