User Groups are used to control what your user can do on the website; for instance, create, edit, and delete articles or categories on the website, work with the menu system, configure extensions, and so on.
The ACL in Joomla 1.5 is hierarchical, each User Group inherits permissions from the group below it. There are only 4 groups available for Public Front–end users and 3 groups for Public Back–end users. The customization of users' groups wasn't possible if you wanted to create a special group for your customers. Each user can be assigned to only 1 defined User Group.

Assign 1 User Group to a new user
The ACL in Joomla 1.7 is not hierarchical; you can build unlimited user–defined groups. A user can be assigned to multiple User Groups with unlimited user–defined Access Levels. User Groups are assigned to Access Levels. Any combination of User Groups can be assigned to any Access Level.
In Joomla 1.7 the User Manager has been extended to 3 sections: Users, User Groups and Viewing Access Levels.

Configure the user's settings with User Manager

Manage user groups easily
As you can see the user can be assigned to several User Groups. Joomla 1.7 allows you to create unlimited User Groups for various needs.

Edit User screenshot
Access Levels control what your user can see on the website. You might restrict the user to see certain categories, articles, menus or components on the website.
Access Levels are fixed and restricted to 3 levels: Public, Registered and Special. The Access Level covers all your articles, component, modules and plugins. Each Access Level belongs to a defined User Group.

Choose predefined Access Level for an article
In Joomla 1.7 you can build unlimited Access Levels with any combination of User Groups can be assigned to them. These settings are located in the menu item Users of the menu toolbar.

Create, edit or delete an Access Level
Let's say we create a new Access Level and name it "Customer Access Level" with assigned groups Manager, Author and Customer Group. Check the necessary box for each User Group and click "Save".

Assign specific User Groups to the Access Level
After creating a new Access Level you can apply it to any articles or categories on the website. Below is the example of setting up the Access Level for an article.

Choose a pre–customized Access Level for an article
The main purpose of Permissions is allowing or denying access to the functionality of your website. For instance, you can allow a User Group to create and edit content only, but restrict access to the components.
Permissions in Joomla 1.5.x has a fixed value and is assigned to defined User Groups. You cannot change or create a new User Groups with preferred permission settings. The permission concept isn't flexible and the customization of user groups is seriously limited.

The permission table of Joomla 1.5
Below you can see the screenshot of a typical interface for Permission Settings. The settings include all created User Groups on your website. For each User Group you can set the Actions and Permission Level.

Action and Permission settings
A User Group has 9 Actions:
The Action has 4 Permissions:
The Joomla 1.7 ACL defines 4 permission levels which can override one another. The low permission level uses the permission from parent level.
Defines the default permission for each user group and actions.

Global Configuration settings
Overrides the default permission for components. For instance, Articles, Menus, Users, Banners and so on.

Components settings
Overrides the permission of Global Configuration and Components. It's available for components with categories including Articles, Contacts, Banners, Newsfeeds, and Weblinks.

Category settings
Overrides the permission of Global Configuration, Components and Category. It's only available for articles in Joomla 1.7 core.

Article settings
With a plain 4-levels structure you can customize permission settings from the smallest object to the biggest one. One thing worth to mentioning here is that with the permission value "inherited" you can configure low-level permissions more effectively and faster.
With the launch of Joomla 1.7 the ACL mechanism added great value to the whole content management system. It gave us more ways to customize the user groups and assign permission for various purposes. Joomla 1.7 ACL is a serious step in the improvement and increased the flexibility of the system. If you have any opinions feel free to share them it out here in the comment box.
Hi TuanBA:
Thank you very much for great article on Joomla 1.7 ACL.
I was trying to understand this new ACL from Joomla 1.6 and was never successful in it. Now after reading your article its more clear. I am going to read this article once again and going to share it to all the joomla community. Its a wonderful effort of explaining new ACL.
Keep up the good work
Regards
Amit Patekar
Excellent article , clearly explained and great detail and diagrams too. Well done
This is an awesome article. Thank you!!

Question though: In this matrix it says (V 1.5) "Author - Edit own content". I know 1.5 will be "end of life" soon, but: Is there a solution for it? I cannot find any website that explains, how Authors can edit their own article.