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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.