The solution that I found for installing qgis (Quantum GIS) on LMDE (Linux Mint Debian Edition) is not optimal, but the only one that worked for me.

I am getting QGIS directly from the QGIS Debian repository and I am temporarily adding the main debian repository to my sources, because QGIS depends on some packages that are not included in LMDE.

LMDE: Install QGIS

1. Add QGIS to your sources.lst:

   sudo vim /etc/apt/sources.list
   # add:
   deb http://qgis.org/debian/ jessie main
   deb http://ftp.us.debian.org/debian/ jessie main
   

After this, do not call apt-get upgrade until you removed these lines.

1. Now you can install QGIS:

   sudo apt-get update
   sudo apt-get install qgis
   

2. And at last remove the added lines from your sources.lst.

   sudo vim /etc/apt/sources.list
   # remove:
   deb http://qgis.org/debian/ jessie main
   deb http://ftp.us.debian.org/debian/ jessie main
   
   sudo apt-get update
   

This step is important, as otherwise a call to apt-get upgrade could break your system.

That’s it, now QGIS should run on your installation of LMDE.