Kodi 17 Krypton is included in Ubuntu repository, which means that you can fast install Kodi in Ubuntu or an Ubuntu-based distro.
Open the terminal (you can press Ctrl+Alt+T) and type in the following:
sudo apt-get install software-properties-common
sudo add-apt-repository ppa:team-xbmc/ppa
sudo apt-get update
sudo apt-get install kodi
Kodi can also be hooked up on different distributions using third-party repositories, but those aren’t formally supported by means of Kodi, so you won’t get the great experience.
you may additionally compile Kodi from source files to run on diverse Linux distros. The official KODI website (here) has a complete guide to installing from the source code.