Introductory course on Unix sysadminning (includes notes, slides, homework, and labs)
ocf.berkeley.edu
ocf.berkeley.edu
As a sysadmin, you are responsible for keeping the show going for a big pile of people, and so you need to make sure that you are visible to those people; that you are more than just a name tagged to an email regarding an outage.
I made it a habit of introducing myself to new users, and of taking a few minutes every day to walk around in a different area of the company, just to see how things were going. On a couple of occasions, this helped me identify a problem before it got big enough to tip off the monitoring software.