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.