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Having run into several references, at various places and occasions, to "Serre’s Course at Collège de France, 19xy-19xy+1" for various values of xy, I would genuinely like to know where these lectures are written down and archived.

Has there been an effort to preserve them in any form?

There are overviews of them in Serre’s collected work, but they have no references and don’t give full proofs.

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    $\begingroup$ Would you be able to provide the overviews that you have found so far? I do not personally know the answer, but it would be helpful for me since I would be able to search via keywords $\endgroup$ – Victoria M Apr 17 at 14:41
  • $\begingroup$ I initially thought that $19xy-19xy+1$ referred to a polynomial, and was very confused. $\endgroup$ – David Zhang Apr 27 at 2:20
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The lecture notes for many of Serre's courses have been published:

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    $\begingroup$ Don't forget 'Algebre locale' (1957 - 1958)! $\endgroup$ – Mere Scribe Apr 17 at 15:12
  • $\begingroup$ Of course for a historical point of view it may be interesting to ask about preserved original versions of these (such as unrevised lectures notes written during the lectures). $\endgroup$ – YCor Apr 17 at 16:53
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    $\begingroup$ There's this recent book about finite group theory by Serre $\endgroup$ – Wilson of Gordon Apr 17 at 20:39
  • $\begingroup$ @CarloBeenakker it was Serre's lecture notes at ENS des Jeunes Files (or some variant plural form...) a basic version is available on arXiv and an expanded version is published $\endgroup$ – Wilson of Gordon Apr 18 at 11:07
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    $\begingroup$ It's not so important, but since you're also linking translations. The first item also exists in translation "Algebraic groups and class field theory", available from Springer. $\endgroup$ – Donu Arapura Apr 18 at 13:44
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The detailed abstracts (résumés détaillés) that are referenced are supposedly available in the "Annuaire du Collège de France". The journal's website unfortunately only contains newer entries (2005–). However, your library might have paper versions. According to Mathdoc, some physical versions are available in a few French libraries (notably at the IHP, the ENS, at the CIRM – with a few gaps in each case, unfortunately).

Some of the published versions that Carlo Beenakker mentions are available at Numdam. You can directly search for Jean-Pierre Serre's works. It might take some digging to know which lecture corresponds to which published paper, but the titles would probably help.

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