This book discusses a variety of problems which are usually treated in a second course on the theory of functions of one complex variable, the level being gauged for graduate students. It treats several topics in geometric function theory as well as potential theory in the plane, covering in particular: conformal equivalence for simply connected regions, conformal equivalence for finitely connected regions, analytic covering maps, de Branges' proof of the Bieberbach conjecture, harmonic functions, Hardy spaces on the disk, potential theory in the plane. A knowledge of integration theory and functional analysis is assumed.

13. Return to Basic 
14.Conformal Equivalence for Simply Connected Regions 
15.Conformal Equivalence for Finitely Connected Regions 
16.Analytic Covering Maps 
17.De Branger;s Proof of the Bieberbach Conjecture 
18.Some Fundamental Concepts from Analysis 
19.Harmonic Functions Redux 
20.Hardy Spaces on the Disk 
21.Potential Theory in the Plane

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