This is a survey of the proof of the global Jacquet-Langlands correspondence between GL_n and general inner forms, in characteristic zero. The proof is given after a long introduction recalling in some detail the objects and results involved. The paper is based on the notes of the lectures I gave at the doctoral school in CIRM 2016 (Jean-Morlet Chair) organized by Dipendra Prasad, Volker Heiermann and Fiona Murnaghan. It appeared in 2018 in the volume Relative Aspects in Representation Theory, Langlands Functoriality and Automorphic Forms (LNM 2221).
Categories: math.NT