Press Ctrl+Alt+F3 and login into the shell.
Now run ls -lah. If in the output the line
-rw------- 1 root root 53 Nov 29 10:19 .Xauthority
then you need to do chown username:username .Xauthority and try logging in.
Else, do ls -ld /tmp. Check for the first 10 letters in the left: they should read exactly so: drwxrwxrwt.
drwxrwxrwt 15 root root 4096 Nov 30 04:17 /tmp
Else, you need to do sudo chmod a+wt /tmp and check again.
If not both, I’d recommend you either
dpkg-reconfigure lightdm- or uninstall, reinstall it.
Now press Alt+-> until you reach the login screen again, and restart.