Cinnamon is the default desktop environment in Linux Mint, it brings the classic Gnome 2 feel to Gnome Shell. The ppa now supports Ubuntu 13.10 Saucy Salamander.
To install Cinnamon session on your Ubuntu, press Ctrl+Alt+T to open terminal, then follow the below steps:
1.) Add the stable ppa repository by running following commands: sudo add-apt-repository ppa:gwendal-lebihan-dev/cinnamon-stable
UPDATE: The PPA has been abandoned, Ubuntu 13.10 user can only install an old version of Cinnamon from Ubuntu repositories by running below commands
2.) Then update the package lists:
sudo apt-get update
3.) Finally install the session:
sudo apt-get install cinnamon
Once installed, log out your current session and select log into Cinnamon on LightDM.