Includes bibliographical references.

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. Seppala; 8. Period matrices and the Schottky problem R. Silhol; 9. Hurwitz spaces S. M. Natanzon.

Presents a cross-section of different aspects of Riemann surfaces, introducing the reader to the basics as well as highlighting new developments in the field. It provides a mixture of classical material, recent results and some non-mainstream topics. The book is based on lectures from the conference Topics on Riemann Surfaces and Fuchsian Groups held in Madrid to mark the 25th anniversary of the Universidad Nacional de Educacion a Distancia. For those wishing to pursue research in this area, this volume offers a valuable summary of contemporary thought and a source of fresh geometric and algebraic insights. The book will be suitable for graduate courses, as well as providing a useful reference for those already working in geometry, group theory, complex analysis, algebraic geometry, topology and theoretical physics.