Login loop with fresh 19.10 install

I had this issue after upgrading from 19.04 to 19.10.

The solution that worked for me is to switch display manager from GDM3 to LightDM.

If you have installed the lightdm package, just run sudo dpkg-reconfigure gdm3 and select LightDM.

After rebooting you should be able to log in.

I have since found a solution to fix login loop without changing GDM3 to LightDM:

Uninstall and reinstall the gdm3 package:

sudo apt-get purge gdm3
sudo apt-get install gdm3

Now just select GDM3, and after a reboot it should work fine.

SOLVED

That's a problem related to the NVIDIA Kernel Module failing with proprietary drivers. To solve it, do the following steps:

At the login screen, press ctrl+alt+f2 to enter the terminal and login with your name and password
Type sudo nano /etc/default/grub (you can change nano to the text editor of your preference) to edit /etc/default/grub
Change the line GRUB_CMDLINE_LINUX_DEFAULT="quiet splash" to GRUB_CMDLINE_LINUX_DEFAULT="nomodeset"
Save the edition pressing ctrl+o and exit pressing ctrl+x
Update this grub edit with sudo update-grub
Install lightdm using sudo apt-get install lightdm
Reboot typing sudo reboot