Several people have asked me for my LaTeX template to write letters, so I guess I might as well put it up on my webpage.
It uses the scrlttr2 package.
I think the markup is relatively self-explanatory.
The template expects a copy of your signature and the logo of your university in the same folder, in images named signature.(png|jpg|...) and logo.(png|jpg|...); this can of course be customized.
If you would like to your letter to be formatted with French norms (recipient on the right, sender on the left, compatible with standard windowed letters), add the NF option to the \documentclass command.
Remember to also change the parameter of the \setmainlanguage command.
Other options are available, see “Letter Class Option Files” in the scrlttr2 manual.
The code is available on GitHub. The end result looks like this PDF.
Since I use polyglossia (for language-specific settings) and unicode-math (for the fonts), the file needs to be compiled with either XeLaTeX or LuaLaTeX.
If you do not want this, then remove these two packages, the \setmainfont and \setmathfont commands, and add the following lines at the beginning of the preamble:
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}