What are the tools, as a system administrator, I can use to keep track of people logging in and those that are trying illegally gain access through the gateway, etc?

Regards,
Mufy

There are all sorts of tools, so you're going to need to be a bit more specific about what you want to do. Monitoring your system logs is always a good first step to see what's going on in your machine. If you're paranoid, you can use syslog to send logged messages to a remote, hardened machine. To see if any files have been modified, there's tripwire, and there's also a program called Snort yhat can help detect intrusions. Snort is a bit complicated, and I've never played with it, so you'll have to look around for more info.