The Jacquet-Langlands correspondence is an important case of the functorial principle in the Langlands program. This book is written by the founder of the eminent French school of automorphic representations and gives an accessible introduction to the Jacquet-Langlands correspondence. It starts from the basic results of automorphic representations and ends with the converse theorem for L-functions. This book is suitable for everyone who is interestedin the Langlands program, in particular automorphic representations, L-functions and the Jacquet-Langlands correspondence. Jacquet-Langlands对应是Langlands 纲领一个重要的函子性原则。本书由自守表示法国学派创始人戈德门特给出的Jacquet-Langlands对应完整的介绍，从自守表示最基本的结论出发，讲到L 函数反定理。

前辅文
1 Representations of the GL2 Group of a p-adic Field
  1. Admissible representations
  2. The Kirillov model: preliminary construction
  3. The commutativity lemma
  4. The finiteness property
  5. Whittaker functions
  6. A theoremon the contragredient of a representation
  7.supercuspidal representations
  8. Introduction to the principalseries
  9. A lemma on Fourier transforms
  10. The principalseries and thespecial representations
  11. The equivalence πμ1,μ2～ πμ2,μ1
  12. The fundamental functional equation
  13. Computation of γπ(χ,s) for the principalseries and the special representations
  14. The local factors Lπ(χ,s)
  15. The factors επ(χ,s)
  16. The case ofspherical representations
  17. Unitary representations: results
  18. Unitary representations: thesupercuspidal case
  19. Unitary representations in the principalseries
  20. Unitary representations: thespecial case
2 The Archimedean Case
  1. Admissible representations
  2. The representations ρμ1,μ2
  3. Irreducible components of ρμ1,μ2 (case F =R)
  4. Irreducible components of ρμ1,μ2 (case F =C)
  5. Kirillov model for an irreducible representation
  6. The functions LW (g;χ,s)
  7. Factors Lπ(χ,s)
  8. Factors επ(χ,s)
3 TheGlobalTheory
  1. Parabolic forms
  2. Local decomposition of an irreducible representation of GA
  3. The globalHecke algebra
  4. GlobalWhittakermodels
  5. Themultiplicity one theorem
  6. Euler product attached to an irreducible representation of GA
  7. The functional equation for Lπ(χ,s)
  8. The converse of Theorem4