弗赖塔格编写的《复分析(2)(英文版)》全面系统地讲述了复分析，从黎曼曲面理论入手，包括单值化理论、对紧黎曼曲面理论的详细论述、黎曼-罗奇定理、Abel定理、Jacobi反演定理。这些内容必引起对多复变数理论的简短介绍，随后讲了Abelian函数理论到θ定理。书的最后部分介绍了高等模函数理论。

本书适合熟悉初级复值函数论基础、椭圆函数理论以及椭圆模函数理论的读者阅读。

Chapter I. Riemann Surfaces

 0 Basic Topological Notions

 1 The Notion of a Riemann Surface

 2 The Analytisches Gebilde

 3 The Riemann Surface of an Algebraic Function

 Appendix A. A Special Case of Covering Theory

 Appendix B. A Theorem of Implicit functions

Chapter II. Harmonic Functions on Riemann Surfaces

 1 The Poisson Integral Formula

 2 Stability of Harmonic Functions on Taking Limits

 3 The Boundary Value Problem for Disks

 4 The Formulation of the Boundary Value Problem on Riemann Surfaces

 and the Uniqueness of the Solution

 5 Solution of the Boundary Value Problem by Means of the

 Schwarz Alternating Method

 6 The Normalized Solution of the External Space Problem

 Appendix. Countability of Riemann Surfaces

 7 Construction of Harmonic Functions with Prescribed

 Singularities: The Bordered Case

 8 Construction of Harmonic Functions with a Logarithmic

 Singularity: The Green's Function

 9 Constrtwtion of Harmonic Functions with a

 Prescribed Singularity: The Case of a Positive Boundary

 10 A Lemma of Nevanlinna

 11 Construction of Harmonic Functions with a Prescribed

  Singularity: The Case of a Zero Boundary

 12 The Most Important Cases of the Existence Theorems

 13 Appendix to Chapter II. Stokes's Theorem

Chapter III. Uniformization

 1 The Uniformization Theorem

 2 A Rough Classification of Riemann Surfaces

 3 Picard's Theorems

 4 Appendix A. The Fundamental Group

 5 Appendix B. The Universal Covering

 6 Appendix C. The Monodromy Theorem

Chapter IV. Compact Riemann Surfaces

 1 Meromorphic Differentials

 2 Compact Riemann Surfaces and Algebraic Functions

 3 The Triangulation of a Compact Riemann Surface Appendix. The Riemann-Hurwitz Ramification Formula

 4 Combinatorial Schemes

 5 Gluing of Boundary Edges

 6 The Normal Form of Compact Riemann Surfaces

 7 Differentials of the First Kind Appendix. The Polyhedron Theorem

 8 Some Period Relations Appendix. Piecewise smoothness

 9 The Riemann-Roch Theorem

 10 More Period Relations

 11 Abel's Theorem

 12 The Jacobi Inversion Problem Appendix. Continuity of Roots

 Appendices to Chapter IV

 13 Multicanonical Forms

 14 Dimensions of Vector Spaces of Modular Forms

 15 Dimensions of Vector Spaces of Modular Forms with Multiplier Systems

Chapter V. Analytic Functions of Several Complex Variables

 1 Elementary Properties of Analytic Functions

 of Several Variables

 2 Power Series in Several Variables

 3 Analytic Maps

 4 The Weierstrass Preparation Theorem

 5 Representation of Meromorphic Functions as Quotients of Analytic Functions

 6 Alternating Differential Forms

 Contents

Chapter VI. Abelian Functions

 1 Lattices and Tori

 2 Hodge Theory of the Real Torus

 3 Hodge Theory of a Complex Torus

 4 Automorphy Summands

 5 Quasi-Hermitian Forms on Lattices

 6 Riemannian Forms

 7 Canonical Lattice Bases

 8 Theta Series (Construction of the Spaces [Q, l, E]) Appendix. Complex Fourier Series

 9 Graded Rings of Theta Series

 10 A Nondegenerateness Theorem

 11 The Field of Abelian Functions

 12 Polarized Abelian Manifolds

 13 The Limits of Classical Complex Analysis

Chapter VII. Modular Forms of Several Variables

 1 Siegel's Modular Group

 2 The Notion of a Modular Form of Degree n

 3 Koecher's Principle

 4 Specialization of Modular Forms

 5 Generators for Some Modular Groups

 6 Computation of Some Indices

 7 Theta series

 8 Group-Theoretic Considerations

 9 Igusa's Congruence Subgroups

 10 The Fundamental Domain of the Modular Group of Degree Two

 11 The Zeros of the Theta Series of Degree two

 12 A Ring of Modular Forms

Chapter VIII. Appendix: Algebraic Tools

 1 Divisibility

 2 Factorial Rings (UFD rings)

 3 The Discriminant

 4 Algebraic Function Fields

References

Index