AUCTeX primarily consists of Lisp files for Emacs, but there are also installation scripts and files and TeX support files. All of those are free; this means that everyone is free to use them and free to redistribute them on a free basis. The files of AUCTeX are not in the public domain; they are copyrighted and there are restrictions on their distribution, but these restrictions are designed to permit everything that a good cooperating citizen would want to do. What is not allowed is to try to prevent others from further sharing any version of these programs that they might get from you.
Specifically, we want to make sure that you have the right to give away copies of the files that constitute AUCTeX, that you receive source code or else can get it if you want it, that you can change these files or use pieces of them in new free programs, and that you know you can do these things.
To make sure that everyone has such rights, we have to forbid you to deprive anyone else of these rights. For example, if you distribute copies of parts of AUCTeX, you must give the recipients all the rights that you have. You must make sure that they, too, receive or can get the source code. And you must tell them their rights.
Also, for our own protection, we must make certain that everyone finds out that there is no warranty for AUCTeX. If any parts are modified by someone else and passed on, we want their recipients to know that what they have is not what we distributed, so that any problems introduced by others will not reflect on our reputation.
The precise conditions of the licenses for the files currently being distributed as part of AUCTeX are found in the General Public Licenses that accompany them. This manual specifically is covered by the GNU Free Documentation License (see Copying this Manual).