Preface; Notation; 1. Compact Riemann surfaces; 2. Group characters; 3. Automorphisms of compact Riemann surfaces; 4. Generation of groups; 5. Classification for small genus; 6. Classification for fixed group: real characters; 7. Classification for fixed group: nonreal irrationalities; Appendix A. Abelian inariants; Appendix B. Irreducible characters; Appendix C. Maillet's determinant; Bibliography; Index.