Enhancing Espers

From an esper's details screen, tap the Enhance button to go to the Enhance screen.

Tap an enhancing material at the bottom of the screen to give it to your esper, which will convert it into experience points.
Magicite can be used to enhance espers, which each type of magicite affecting each esper differently.
Particularly effective magicite are labeled with text such as 1.5x EXP, so be sure to choose the most effective ones.

Espers level up when they reach the maximum experience points for each level.
Whenever espers level up, their stats also rise.
They also gain a certain amount of SP whenever they level up.
The amount of SP that can be gained also varies by esper.