The Crystarium is a character’s growth chart, with which you can buy various upgrade nodes:

• **Ability** node teaches character a new ability.
• **HP** node increases character's maximum HP.
• **Strength** node increases character's Strength stat.
• **Magic** node increases character's Magic stat.
• **Accessory** node increases character's accessory slots by 1.
• **ATB** node increases number of segments in chraracter's ATB gauge by 1.
• **Role** node raises character's role level by 1.

You can purchase nodes by expending CP, which are obtained by winning battles. The characters' growth is fairly linear, with the odd path branching off here and there. Note that some abilities are not available to all characters - for example, Vanille is the only one who gets access to the Death spell.

See the Crystarium section of the guide for a detailed look at an optimal progression through the game for each character.