Cover; Title page; Preface; Chapter 1. Introduction; Chapter 2. An overview; Chapter 3. Extremal problems in the symmetrized bidisc; 3.1. The Carathéodory and Kobayashi extremal problems; 3.2. The Carathéodory extremal problem () for; 3.3. Five types of datum in; 3.4. The Kobayashi extremal problem () for; Chapter 4. Complex geodesics in; 4.1. Complex geodesics and datums in; 4.2. Uniqueness of complex geodesics for each datum in; 4.3. Flat C-geodesics; 4.4. Rational \Ga-inner functions; Chapter 5. The retracts of and the bidisc ²; 5.1. Retracts and geodesics of
5.2. Retracts of ²5.3. Geodesics in are varieties; Chapter 6. Purely unbalanced and exceptional datums in; Chapter 7. A geometric classification of geodesics in; Chapter 8. Balanced geodesics in; Chapter 9. Geodesics and sets with the norm-preserving extension property in; 9.1. and ( ); 9.2. and balanced datums; 9.3. and flat or royal datums; Chapter 10. Anomalous sets ℛ∪ with the norm-preserving extension property in; 10.1. Definitions and lemmas; 10.2. The proof of the norm-preserving extension property for \calr∪\cald
