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O. Introduction and statement of main results 1. Horocyclic coordinates 2. The zw = t plumbing construction 3. The plumbing construction for an admissible graph 4. Deformation (TeichmiiUer) and moduli (Riemann) spaces 5. Torsion free terminal b-groups 6. One-dimensional deformation spaces 7. Deformation spaces for torsion free terminal b-groups 8. One-dimensional moduli spaces 9. Moduli spaces for torsion free terminal b-groups 10. Forgetful maps 11. Metrics on surfaces and their Teichmiiller spaces 12. Appendix I: Calculations in PSL(2, C) and SL(2, C) 13. Appendix II: A computer program for computing torsion free terminal bgroups 14. Appendix III: Independence of gluing on choice of annuli

Horocyclic coordinates for Riemann surfaces and moduli spaces. I. Teichmüller and Riemann spaces of Kleinian groups