Square Enix revealed the character growth system in Final Fantasy XIII, it is called the Crystalium System, which replaces the character level-up system and resembles the Sphere Grid system used in Final Fantasy X. After each battle you earn Crystalium Points (CPs), which can be spent in the Crystalium System to acquire new abilities. New abilities become available once you learned certain abilities in the grid.
There will be an amusement park in the game's Cocoon city, which seems to have a lot of facilities and a video wall, which shows videos of the summon beasts.
In addition the magic level-up is demonstrated in the Crystalium System, you start with Fire, and you can learn Fira by level-up the blaster role, and it can be further upgraded to Firaga, which can hit multiple enemies and blast them into the mid-air.