Robert P. Langlands

Author's comments: Some surprise has been expressed that the notes of Jacquet-Langlands have been placed in the same section as the notes on the $\epsilon$-factor. There is a good reason for this. Although the notion of functoriality had been introduced in the original letter to Weil, there were few arguments apart from aesthetic ones to justify it. So it was urgent to make a more cogent case. One tool lay at hand, the Hecke theory, in its original form and in the more precise form created by Weil.

Author's comments: This paper is quite informal and I could not immediately reflect on the suggestions it contains. I am grateful to Freydoon Shahidi for suggesting that as an interim measure I write the paper for submission to the Canadian Mathematical Bulletin, where it appeared in volume 50 (2007).

Editorial comments: In January of 1967, while he was at Princeton University, Langlands wrote a letter of 17 hand-written pages to Andre Weil outlining what quickly became known as `the Langlands conjectures'. This letter even today is worth reading carefully, although its notation is by present standards somewhat clumsy. It was in this letter that what later became known as the `$L$-group' first made its appearance, like Gargantua, surprisingly mature.