In my emacs 24.3, I can't find the AUCTeX package. If I enter PACKAGE-LIST-PACKAGE, I find various packages for AUCTeX like "auctex-lua" or "auto-complete for auctex". However, there is no auctex package that I can install. Why is it gone ?
AUCTeX is available via GNU ELPA, not MELPA.
You can configure multiple repositories, e.g. by using add-to-list instead of setting package-archives directly:
(add-to-list 'package-archives
'("melpa" . "http://melpa.org/packages/") t)
This should keep GNU ELPA in your list of archives, but in case it doesn't you can always add it back. It should look something like
("gnu" . "http://elpa.gnu.org/packages/")
Once you've done this you should be able to install AUCTeX via package.el.
Note that this is likely the one repository that most users should have in their package-archives list. It's the official GNU repository, enabled by default. Of course, feel free to add others as you wish!