Most Linux distributions carry a version of Emacs.

In case the version coming with your Linux distribution is outdated, you might want to build from source.

If you would not like to build from source, you can use the Emacs AppImage provided at https://github.com/probonopd/Emacs.AppImage. To use it, simply download it, set the executable bit (e.g., using the GUI or chmod a+x), and execute it.