Safety issues in PHP log-in system
MVC
If you're trying to make a CMS, then there's a possibility that this CMS will become bigger than you first though. More pages, more modules, more code. You might want to consider doing an MVP approach to splitting code (rather than MVC).
A good reference framework for this is CodeIgniter. Presenter (CodeIgninter calls it the Controller) receives a request, then operates the data on the model (the model layer + database), then grabs a view (A template, your HTML) and renders it (&quot;echo&quot; the template).
SQL Injection
Then I notice this part:
$sql    = 'SELECT * FROM utilizatori '; 
$sql   .= 'WHERE user = &quot;'.self::$_user.'&quot; AND password = &quot;'.self::$_password.'&quot; ';

You should read more about SQL injection. In a gist, it allows users to run arbitrary SQL, even be able to fake logins, see through existing usernames and passwords, as well as drop entire databases.
Sessions
Then there's sessions. For simple situations, that's fine. But for security, there's a lot to consider. If I can shoot malicious code through the forms, then I just might be able to fake my session. Read on this post for things to consider with sessions.
Validation
I see you use strip_tags() but it only does what it does, strip tags. It does not strip the other stuff, like backticks and quotes which can still be used to break in. A good example is the story of Little Bobby Tables. No tags, still broke through the database.
Redirect
window.location = &quot;admin.php&quot;

This operates on the browser. This means that index.php is actually served before redirecting, possibly rendering the page before this runs. I suggest you do a header redirect. It does not serve the page to the browser. It just tells the browser directly to load another page instead.