I want to enable auto-logon with root user for some specific purpose. It's so boring that every time I power on my PC to study, I have to input user and password.
I'd recommend you to still use a regular user, but to configure sudo without password. Anytime you need to do a root command, you can just do:
# sudo command
If you want to have a terminal opened with sudo shell, do
# sudo bash
Note this is still giantic hole in the security of your system :-) As root do:
and add this line:
yourusername ALL=NOPASSWD: ALL
If you like this solution, you can maybe slightly increase the security by configuring long timeout for passwords. So you only will be asked one an hour/day or week.