* Preface Part I: Classical Function Theory * Invariant Geometry * Variations on the Theme of the Schwarz Lemma * Normal Families * The Riemann Mapping Theorem and its Generalizations * Boundary Regularity of Conformal Maps * The Boundary Behavior of Holomorphic Functions Part II: Real and Harmonic Analysis * The Cauchy-Riemann Equations * The Green's Function and the Poisson Kernel * Harmonic Measure * Conjugate Functions and the Hilbert Transform * Wolff's Proof of the Corona Theorem Part III: Algebraic Topics * Automorphism Groups of Domains in the Plane * Cousin Problems, Cohomology, and Sheaves * Bibliography * Index

* Presented from a geometric analytical viewpoint, this work addresses advanced topics in complex analysis that verge on modern areas of research

* Methodically designed with individual chapters containing a rich collection of exercises, examples, and illustrations