Kodi on (a vergin) Debian Jessie 8.3

We do it throught the debian multimedia repository.
So open in editing the /etc/apt/sources.list file and add at the end this row

deb http://www.deb-multimedia.org jessie main non-free

Then 
apt-get install deb-multimedia-keyring 
apt-get update
apt-get upgrade

Finally:
apt-get install kodi

Optional
if you know that you will use your kobi also for live tv you need to install a PVR add-on that in linux installer there aren't bundled.
Here is an example for iptv addon

apt-get install kodi-pvr-iptvsimple

Please refere here for the pvr addons available.. 
Bye..