I am doing a documentation about Adobe Experience Manager and I want it to be public on Github, but I don't know if this is possible because of the privative software.
Can I upload it? If so, do I need a special license?
Why not? There are a number of blogs available to the public, and I am not aware that they needed to sign a special contract or so.
Adding to what Jörg said, You can refer to the official docs at