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Preface Introduction A. F. Beardon 1. The geometry of Riemann surfaces A. F. Beardon 2. Introduction to arithmetic Fuchsian groups C. Maclachlan 3. Riemann surfaces, Belyi functions and hypermaps D. Singerman 4. Compact Riemann surfaces and algebraic function fields P. Turbek 5. Symmetries of Riemann surfaces from a combinatorial point of view G. Gromadzki 6. Compact Klein surfaces and real algebraic curves F. J. Cirre and J. M. Gamboa 7. Moduli spaces of real algebraic curves M. Seppa;la; 8. Period matrices and the Schottky problem R. Silhol 9. Hurwitz spaces S. M. Natanzon.