I am looking for a CMS - user management - that will allow me to to add users and allow them the possibility of created an extensive user profile . Basically, I am looking for a user management script - or CMS - with heavy customization options.
Basically, what I want to do is something like a social network, but very private. It will be used at a local school.
If you know something that can help me achieve this, I would greatly appreciate it.
I think you're describing Drupal.
One of Drupal's strongest points is robust user management. With Drupal you can have as many user types (roles) as you like and then assign the roles granular permissions with what they can see and do on the site. The administration tools allows you to configure user accounts with as many fields as you need for users to fill in on their profiles. You can extend profiles with the profiles module or you can add a full on CRM to the back end (civiCRM) so that users get a contact dashboard for managing memberships, groups, events, relationships, etc...
Drupal - https://drupal.org/
Profile 2 (for extending profiles) - https://drupal.org/project/profile2
CiviCRM - https://civicrm.org/
Edit: I thought I would add to more thoughts:
Thanks. It seems Drupal was exactly what I was looking for!
Great! It can be pretty addictive once you get the hang of it. The install profiles tend to be pretty purpose built so most of the configuration will be done for you. That said, it wouldn't hurt to get a book or two on the CMS to get you up to speed on best practices. I'd recommend Using Drupal from O'Reilly: http://www.usingdrupal.com/. It starts at the very basics but it does a good job of explaining the best way to go about using the system.