Question: My Debian doesn't boot with a GUI

Answer

If you expect your machine to boot with a GUI and it doesn’t you might need to look at which Display Manager (aka dm) you have installed:

dpkg -l | awk '/^ii .*dm / { print $2}'

If you run X11, you can also inspect the file /etc/X11/default-display-manager to see which is your default:

$ cat /etc/X11/default-display-manager
/usr/sbin/lightdm

If that returns some thing, do this: systemctl status <what you got as answer>. In my case that would be: systemctl status lightdm. That should give you some output, similar to this:

$ systemctl status lightdm
● lightdm.service - Light Display Manager
     Loaded: loaded (/usr/lib/systemd/system/lightdm.service; enabled; preset: enabled)

If it isn’t enabled, do systemctl enable lightdm. Reboot to confirm your GUI boots.

Alternatively it could be that your target is incorrect, please check that systemctl get-default returns graphical.target. If it is multi-user.target, please set it to graphical: systemctl set-default graphical.target.