An Introduction to Analytic Functions with Theoretical Implications

0. Conventions, Set Theory, Number Systems.- 1. The Complex Plane, Relations, Functions.- 2. Boundedness, Convergence, Continuity.- 3. Paths, Integrals, Derivatives.- 4. Connectedness, Convexity, Analyticity.- 5. Triangles, Polygons, Simple Regions.- 6. Extensions, Contours, Elementary Functions.- 7. Power-Series, Residues, Singularities.- 8. Analytic Inverses, Standard Regions, Convergence Continuation.- 9. Extended Complex Plane, Linear-Fractional Transformations, Meromorphic Functions.- 10. Analytic Relations, Analytic Continuation, Functional Boundaries, Branch-Points.- Appendix A. Homotopy Groups.- Appendix B. Automorphic Functions.- Appendix C. Excepted Values and Uniformization.- Appendix D. Well-ordering.- Appendix E. Analytic Surfaces.- Mac Nerney's Theorem Numbering in the original Edition.- Index.