Paradigms
The Paradigm system is introduced in Chapter 3 in the game and it marks where you can begin to select different job combinations (referred to as Roles in Final Fantasy XIII) for your characters. Use the link below for an explanation of how the Paradigm system works:
Paradigm Explanation

An overview of the Paradigm system in Final Fantasy XIII that expands on the tutorial and Primer provided in the game’s Datalog.
You can use the links below for a full list of the paradigms you can create as well as the link below that for common and recommended paradigms:
Common and Recommended Paradigms

Not all paradigms are created equal. Which paradigms should you use for your party considering that you have a maximum of six that you can setup?
Finally, a separate page has been setup that provides a high level overview of advanced paradigm tactics that you can employ:
Advanced Paradigm Tactics
Tips and Tricks

Tips and tricks you can utilize during a play through to make the most effective use of paradigms.