亚纯函数（meromorphic function）是在区域D上有定义，且除去极点之外处处解析的函数。

本书系统地讲述了复变函数中亚纯函数的值分布理论。全书共分七章，主要包括：亚纯函数及其连接；T方向与分布值和亏值总数的关系；射线分布值确定亚纯函数的增长性的问题等内容。

本书共7章，研究在复平面上或在以原点为顶点的角域上亚纯的函数的值分布，即通过某些值点来刻画亚纯函数。前两章研究各类特征函数及这样的实函数的性质。第3、4章放在新引入的奇异方向——T方向，包括存在性、分布，与其他方向的关系上，T方向与分布值和亏值总数的关系。射线分布值确定亚纯函数的增长性的问题在第5章详细研究。第6章研究亚纯函数对应的Riemann曲面，逆函数的奇异性及其与不动点的关系。最后一章介绍具有重要地位的ENevanlinna猜想的Eremenko应用位势论的证明。

1 Preliminaries of Real Functions

 1.1 Functions of a Real Variable

1.1.1 The Order and Lower Order of a Real Function

1.1.2 The P61ya Peak Sequence of a Real Function

1.1.3 The Regularity of a Real Function

1.1.4 Quasi-invariance of Inequalities

 1.2 Integral Formula and Integral Inequalities

1.2.1 The Green Formula for Functions with Two Real Variables

1.2.2 Several Integral Inequalities

 References

2 Characteristics of a Meromorphic Function

 2.1 Nevanlinna's Characteristic in a Domain

 2.2 Nevanlinna's Characteristic in an Angle

 2.3 Tsuji's Characteristic

 2.4 Ahlfors-Shimizu's Characteristic

 2.5 Estimates of the Error Terms

 2.6 Characteristic of Derivative of a Meromorphic Function

 2.7 Meromorphic Functions in an Angular Domain

 2.8 Deficiency and Deficient Values

 2.9 Uniqueness of Meromorphic Functions Related to Some Angular Domains

 References

3 T Directions of a Meromorphic Function

 3.1 Notation and Existence of T Directions

 3.2 T Directions Dealing with Small Functions

 3.3 Connection Among T Directions and Other Directions

 3.4 Singular Directions Dealing with Derivatives

 3.5 The Common T Directions of a Meromorphic Function and Its Derivatives

 3.6 Distribution of the Julia, Borel Directions and T Directions

 3.7 Singular Directions of Meromorphic Solutions of Some Equations

 3.8 Value Distribution of Algebroid Functions

 References

4 Argument Distribution and Deficient Values

 4.1 Deficient Values and T Directions

 4.2 Retrospection

 References

5 Meromorphic Functions with Radially Distributed Values

 5.1 Growth of Such Meromorphic Functions

 5.2 Growth of Such Meromorphic Functions with Finite Lower Order

 5.3 Retrospection

 References

6 Singular Values of Meromorphic Functions

 6.1 Riemann Surfaces and Singularities

 6.2 Density of Singularities

 6.3 Meromorphic Functions of Bounded Type

 References

7 The Potential Theory in Value Distribution

 7.1 Signed Measure and Distributions

 7.2 δ-Subharmonic Functions

7.2.1 Basic Results Concerning 8-Subharmonic Functions

7.2.2 Normality of Family of 8-Subharmonic Functions

7.2.3 The Nevanlinna Theory of 8-Subharmonic Functions

 7.3 Eremenko's Proof of the Nevanlinna Conjecture

 References

Index