●PREFACE
INDEX OF NOTATION
1 TOPOLOGICAL GROUPS
1.1 Basic Notions
1.2 Haar Measure
1.3 Profinite Groups
1.4 Pro-p-Groups
Exercises
2 SOME REPRESENTATION THEORY
2.1 Representations of Locally Compact Groups
2.2 Banach Algebras and the Gelfand Transform
2.3 The Spectral Theorems
2.4 Unitary Representations
Exercises
3 DUALITY FOR LOCALLY COMPACT ABELIAN GROUPS
3.1 The Pontryagin Dual
3.2 Functions of itive Type
3.3 The Fourier Inversion Formula
3.4 Pontryagin Duality
Exercises
4 THE STRUCTURE OF ARITHMETIC FIELDS
4.1 The Module Of an Automorphism
4.2 The Classification ofLocally Compact Fields
4.3 Extensions of Local Fields
4.4 Places and Completions of Global Fields
4.5 Ramification and Bases
Exercises
5 ADELES,IDELES,AND THE CLASS GROUPS
5.1 Restricted Direct Products,Characters,and Measures
5.2 Adeles,Ideles,and the Approximation Theorem
5.3 The Geometry of Ak/K
5.4 The Class Groups
Exercises
6 A QUICK TOUR 0F CLASS FIELD THEORY
6.1 Frobenius Eiements
6.2 The Tchebotarev Density Theorem
6.3 The Transfer Map
6.4 Artin's Reciprocity Law
6.5 Abelian Extensions of Q and Qp
Exercises
7 TATE'S THESIS AND APPLICATIONS
7.1 Local-Functions
7.2 The Riemann-Roch Theorem
7.3 The Global Functional Equation
7.4 Hecke L-Functions
7.5 The Volume of C and the Regulator
7.6 Dirichlet'S Class Number Formula
7.7 Nonvanishing on tile Line Re(s)=1
7.8 Comparison of Hecke L-Functions
Exercises

本書是一部學習數論和群論的研究生教程。每章的引入十分有意思，對歷史材料的深入理解和作者對相關內容獨到的理解和表達方式，使得本書組成一個有機的整體，這些正是一個初學者所需要的。同時，這本書也很適合於科研人員。書中包括了不少比較復雜的內容，使得這本書的部分內容比較難懂，也是本書吸引讀者的一個原因。每章的後面都附有習題。讀者對像：數學專業的研究生，教師和相關專業的科研人員。