Paradigm Roles
Each character's Crystarium has six separate development paths, corresponding to the paradigm roles they can cover: Commando, Ravager, Sentinel, Synergist, Saboteur and Medic. Each path contains both passive stat bonuses and abilities; although every character in the game can cover every role, to perform a role well, the character needs to obtain role-specific abilities through the Crystarium. Each character has three primary and three secondary roles. Unlocking nodes in the development path for a character's primary roles costs fewer crystogen points. Additionally, primary paths for each role offer more abilities than secondary paths for the same role. However, some useful abilities, such as the Sentinel ability "Elude," are available only to characters for whom the role counts as a secondary.
Development
Crystarium paths are formed by separate circular levels, with the center node of each level leading to a node on the circumference of the next. Before you can move on to the next level, you must activate all the nodes on the circumference of the current level. While the paths for each character's secondary roles are linear, primary role paths contain optional nodes that branch away from the circumference. These nodes are not required to proceed to the next level; however, they often contain additional abilities.
Special Nodes
Certain paths within the Crystarium contain special nodes, providing quality of life upgrades rather than abilities or attribute increases. Each character has access to one ATB Level node, always found in a primary role path, which increases the length of that character's ATB bar by one. Additionally, each path has four Role Level nodes. These nodes improve the character's overall performance in that role; as long as the character who activated the Role Level node for a specific role is in the party and fulfilling that role, the performance of other characters in the party will also be slightly improved in the same way, even if the other characters aren't currently covering that role. By developing primary roles, each character can also obtain three additional Accessory slots, allowing her to equip a total of four Accessories, and a single unique ability specific to that character. These abilities are role-specific and can only be used if you are controlling that character directly as the party leader.
Level Acquisition
The Crystarium becomes available at the beginning of Chapter 3. However, each character can originally develop only a limited number of roles. The three primary roles are unlocked over the course of Chapters 3 and 4, and the three secondary ones at the start of Chapter 10. Initially, each character only has access to one Crystarium level per path. The second level becomes available at the end of Chapter 3, the third level during Chapter 4 and the fourth at the end of Chapter 5. Completing Chapters 6, 7 and 9 respectively unlocks the fifth, sixth and seventh levels; the eight level is unlocked during Chapter 10, the ninth at the end of Chapter 11 and the tenth and final one at the end of Chapter 13, the last chapter in the game.
Considerations
Deciding early on in the game which roles you want to use for each character will allow you to focus on developing those roles first rather than spend points to improve a role you never use. It's fully possible to complete the game without completing the Crystarium. However, the "Master's Seal" achievement for the Xbox 360 and a Silver Trophy of the same name for the PlayStation 3 are rewarded for fully developing all characters' Crystarium paths, activating all nodes including the optional ones. This can only be done after the end of the game and requires a significant amount of crystogen points. The Growth Egg accessory, rewarded from completing the Cie'th Stone Mission 55, doubles the amount of crystogen points you gain from battles and will make it easier for you to develop your characters.