奇尔德雷斯编著的《类域论》将Gauss、Legendre和其他的二次和更高阶的互反率巧妙结合，并将这些结果更加一般化，是学习类域理论的入门书籍。本书运用传统方法和原始技巧呈现书中的材料，思路清晰流畅，是这个领域的图书很难企及的。本书可以作为代数数论的研究生教程，尤其适合自学。书中有大量的练习贯穿始终，已经被证明了是一本很成功的教材。

1 A Brief Review

 1 Number Fields

 2 Completions of Number Fields

 3 Some General Questions Motivating Class Field Theory

2 Dirichlet's Theorem on Primes in Arithmetic Progressions

 1 Characters of Finite Abelian Groups

 2 Dirichlet Characters

 3 Dirichlet Series

 4 Dirichlet's Theorem on Primes in Arithmetic Progressions

 5 Dirichlet Density

3 Ray Class Groups

 1 The Approximation Theorem and Infinite Primes

 2 Ray Class Groups and the Universal Norm Index Inequality

 3 The Main Theorems of Class Field Theory

4 The Idelie Theory

 1 Places of a Number Field

 2 A Little Topology

 3 The Group of Ide1es of a Number Field

 4 Cohomology of Finite Cyclic Groups and the Herbrand Quotient

 5 Cyclic Galois Action on Ideles

5 Artin Reciprocity

 1 The Conductor of an Abelian Extension of Number Fields and the Artin Symbol

 2 Artin Reciprocity

 3 An Example: Quadratic Reciprocity

 4 Some Preliminary Results about the Artin Map on Local Fields

6 The Existence Theorem, Consequences and Applications

 l The Ordering Theorem and the Reduction Lemma

 2 Kummer n-extensions and the Proof of the Existence Theorem

 3 The Artin Map on Local Fields

 4 The Hilbert Class Field

 5 Arbitrary Finite Extensions of Number Fields

 6 Infinite Extensions and an Alternate Proof of the Existence Theorem.

 7 An Example: Cyclotomic Fields

7 Local Class Field Theory

 1 Some Preliminary Facts About Local Fields

 2 A Fundamental Exact Sequence

 3 Local Units Modulo Norms

 4 One-Dimensional Formal Group Laws

 5 The Formal Group Laws of Lubin and Tare

 6 Lubin-Tate Extensions

 7 The Local Artin Map

Bibliography

Index