\"《代数函数与Abelian函数导论(第2版)(英文版)》讲述了：This short book gives an introduction to algebraic and abelian functions, withemphasis on the complex analytic point of view. It could be used for a course　or seminar addressed to second year graduate students.\"

Chapter Ⅰ　The Riemann-Roch Theorem 1. Lemmas on Valuations 2. The Riemann-Roch Theorem 3. Remarks on Differential Forms 4. Residues in Power Series Fields 5. The Sum of the Residues 6. The Genus Formula of Hurwitz 7. Examples 8. Differentials of Second Kind 9. Function Fields and Curves 10. Divisor Classes Chapter Ⅱ　The Fermat Curve 1. The Genus 2. Differentials 3. Rational Images of the Fermat Curve 4. Decomposition of the Divisor Classes Chapter Ⅲ　The Riemann Surface 1. Topology and Analytic Structure 2. Integration on the Riemann Surface Chapter Ⅳ　The Theorem of Abel-Jacobi 1. Abelian Integrals 2. Abel\'s Theorem 3. Jacobi\'s Theorem 4. Riemann\'s Relations 5. Duality Chapter Ⅴ　Periods on the Fermat Curve 1. The Logarithm Symbol 2. Periods on the Universal Covering Space 3. Periods on the Fermat Curve 4. Periods on the Related Curves Chapter Ⅵ　Linear Theory of Theta Functions 1. Associated Linear Forms 2. Degenerate Theta Functions 3. Dimension of the Space of Theta Functions 4. Abelian Functions and Riemann-Roch Theorem on the Toru 5. Translations of Theta Functions 6. Projective Embedding Chapter Ⅶ　Homomorphisms and Duality 1. The Complex and Rational Representations 2. Rational and p-adic Representations 3. Homomorphisms 4. Complete Reducibility of Poincar 5. The Dual Abelian Manifold 6. Relations with Theta Functions 7. The Kummer Pairing 8. Periods and Homology Chapter Ⅷ　Riemann Matrices and Classical Theta Functions 1. Riemann Matrices 2. The Siegel Upper Half Space 3. Fundamental Theta Functions chapterⅨ Involutions and Abelian Manifolds of Quaternion Type 1. Involutions 2. Special Gnerators 3. Orders 4. Lattices and Riemann Forms on Determined by Quaternion Algebras 5. Isomorphism Classes chapteⅩ Theta Functions and Divisors I. Positive Divisors 2. Arbitrary Divisors 3. Existence of a Riemann For