Please discuss the use of a root account in Ubuntu. For example, following a standard installation, I added a second account, then tried to remove it. But it won't go away since I am not root

Ubuntu doesn't really install a root with passeord. To run commands that require root use sudo before the command. Example.
sudo ifconfig eth0

Brian

Did you use sudo to remove the second account?

Under Ubuntu you are supposed to use "sudo" for all superuser access. It is supposed to be set up by default to allow the first created user account to use sudo. I haven't used Ubuntu recently so I am unsure of how it is supposed to work currently, but I remember I got around Ubuntu's various root user problems by creating a password for root so I could log in as root and do maintenance. This is probably not "good practice" but it works for me. You can also swap to a root (console) login with the command sudo su -, which should dump you in a root login shell.

or just sudo -i

Everything you need to know is here:
https://help.ubuntu.com/community/RootSudo
http://www.psychocats.net/ubuntu/permissions
http://psychocats.net/ubuntu/security#sudoisnotroot

Why not just go to System > Administration > Users & Groups to remove the user?

thank you for the fast help. I tried the System > Administration > Users and Groups right away and the second user came back to life on his own unfortunetly

I will use the sudo from now on. My concern is that I was supposed to set up a root account but couldn't figure out how.

Then you have nothing to worry about. You weren't supposed to set up a root account.

You don't have to setup a root account on Ubuntu, but many people who are used to a classical root account may prefer it over sudo. It just depends on what you are comfortable with. Personally I disable sudo when I setup Ubuntu based systems for myself and use classical root. To run commands as root, I use 'su -c' so there is no need to login as root proper.