How to grant access on some functionnalities in system dashboard to a given role How can I grant access on system dashboard to a given role.
Let's assume the role is "Webmaster". So when a user with this role logged in, he will land to the admin page as if he belongs to the "admin" role, but with fewer options available.
For example he will not be able to see the "configuration" menu, and so fourth...

Because what I actually have is, when this kind of user logged in, he lands on a user page like other authenticated user (I mean a regular front page).

Thanks for your help
By default, when a user logs in on Drupal, they are redirected to /user (the user page). If you want to change that behavior (so they are redirected to a custom dashboard page that you create (ie: /admin/dashboard) you might be able to use Rules (assuming you are on D7 - Rules is not ready for D8 yet as far as I know). You would create a Rule that triggers when a user logs in, add a condition to check there role, and an action to redirect them to another page.

You may also want to read this, because there may be more conditions you want to include, so that they are NOT redirected when they are resetting their password, for example: https://www.drupal.org/node/480584

As for hiding Configuration menu and other things, that is accomplished by assigning (or not assigning) permissions to the user roles. So your admin role should include access to Configuration, but your other roles should not.