It appears as if a package may have been corrupted during the install.
Try manually running gdm
First thing to try is to manually invoke gdm:
sudo service gdm restart
if this fails, look at the errors with:
sudo service gdm status
and post them, or continue with the other steps.
Fixing most broken packages
Most broken packages can be fixed with a simple:
sudo apt install -f
Reinstalling
If apt install -f doesn't help, then try reinstalling gdm, the display manager:
sudo apt install --reinstall gdm
Try lightdm
As I've personally haven't had much experience with Ubuntu 17.10, I'm not sure if this would work, but it's worth a shot:
sudo apt install lightdm
This will install lightdm, the display manager used before ubuntu switched to gdm.
dpkg --reconfigure -a? and doing an autoremove? – Abel Tom May 24 '18 at 06:23