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Fundamentals Of Linux

The different commands for Monitoring the Users

Users monitoring & logging
Log login attempts try
To log - login or tried attempts, that create the file /var/log/wtmp.
To log - bad login input or attempts, create the file /var/log/btmp.
To view or monitor all related authentication information – The file location would be at the /var/log/auth.log file ( need to install logwatch this might be a good choice or idea to simplify your log monitoring).

Prevent against brute force attacks
Limit the maximum fail login attempts using faillog. If the  limit the maximum failed login attempts to 5 :  faillog -m 5 -u "$USER"
There are numerous more ways to succeed account security on a Linux box. These few points might, however, be very helpful to a Linux admin beginner.