Preface to the Series Preface to Part 2 Chapter 12.Riemannian Metrics and Complex Analysis §12.1.Conformal Metrics and Curvature §12.2.The Poincare Metric §12.3.The Ahlfors-Schwarz Lemma §12.4.Robinson's Proof of Picard's Theorems §12.5.The Bergman Kernel and Metric §12.6.The Bergman Projection and Painleve's Conformal Mapping Theorem Chapter 13.Some Topics in Analytic Number Theory §13.1.Jacobi's Two-and Four-Square Theorems §13.2.Dirichlet Series §13.3.The Riemann Zeta and Dirichlet L-Function §13.4.Dirichlet's Prime Progression Theorem §13.5.The Prime Number Theorem Chapter 14.Ordinary Differential Equations in the Complex Domain §14.1.Monodromy and Linear ODEs §14.2.Monodromy in Punctured Disks §14.3.ODEs in Punctured Disks §14.4.Hypergeometric Functions §14.5.Bessel and Airy Functions §14.6.Nonlinear ODEs: Some Remarks §14.7.Integral Representation Chapter 15.Asymptotic Methods §15.1.Asymptotic Series §15.2.Laplace's Method: Gaussian Approximation and Watson's Lemma §15.3.The Method of Stationary Phase §15.4.The Method of Steepest Descent §15.5.The WKB Approximation Chapter 16.Univalent Functions and Loewner Evolution §16.1.Fundamentals of Univalent Function Theory §16.2.Slit Domains and Loewner Evolution §16.3.SLE: A First Glimpse Chapter 17.Nevanlinna Theory §17.1.The First Main Theorem of Nevanlinna Theory §17.2.Cartan's Identity §17.3.The Second Main Theorem and Its Consequences §17.4.Ahlfors' Proof of the SMT Bibliography Symbol Index Subject Index Author Index Index of Capsule Biographies