0. Introduction -- 1. Basic Concepts -- 2. Conformal Mappings -- 3. Schwarzโ{128}{148}Christoffel Integrals -- 4. Polynomial Approximations -- 5. Nearly Circular Regions -- 6. Greenโ{128}{153}s Functions -- 7. Integral Equation Methods -- 8. Theodorsenโ{128}{153}s Integral Equation -- 9. Symmโ{128}{153}s Integral Equation -- 10. Airfoils -- 11. Doubly Connected Regions -- 12. Singularities -- 13. Multiply Connected Regions -- 14. Grid Generation -- Appendix A. Cauchy P. V. Integrals -- A.1. Numerical Evaluation -- Appendix B. Greenโ{128}{153}s Identities -- Appendix C. Riemannโ{128}{148}Hilbert Problem -- C.1. Homogeneous Hilbert Problem -- C.2. Nonhomogeneous Hilbert Problem -- C.3. Riemannโ{128}{148}Hilbert Problem -- Appendix D. Successive Approximations -- D.1. Tables -- Appendix E. Catalog of Conformal Mappings -- Bibliography 431 Notation