As you play the game, you'll find, buy, and be given Materia Orbs. When equipped, these orbs have various functions (like Relics from FF3), and become stronger as you use them (like the Classes from FF5j). There are five types of Materia:

	Spell Materia	When equipped, you can cast spells like Lightning, Fire, Cure, Barrier, etc.
	Command Materia	These give you the ability to Steal, Throw, Mimic, etc.
	Independent Materia	These will increase your scores, like Max HP or Speed Plus.
	Support Materia	These augment the power of certain other Materia. For instance, the 'Select All' Materia, when combined with a Fire materia, lets you cast a fire spell on all foes.
	Summon Materia	These let you summon monsters, like Chocobo, Shiva, Bahamut, or even Typoon!

You can equip Materia from the Main Menu, and mix and match them in any way you want. This is how they work:

Weapons and bracelets have a certain number of 'holders' on them. You can equip one Materia per holder. So, if a sword has one holder and a bracelet has five holders, you can equip six Materia in all. The benefit to equipping a Materia is the skills/magic/etc. it gives you. The bad part is that equipping Materia tends to lower your statistics. While this is only temporary, you'll have to decide if you value skills or scores more when equipping certain Materia. To restore your stats. to normal, simply unequip the Materia you're using. You'll notice that some holders aren't connected, and some are (it looks something like this: 0=0 ). Connected holders are used to couple an Independent Materia with another Materia, since Independent Materia have no effect on their own.

When you win a battle, you gain AP (Ability Points). Each Materia has a number of stars, representing its' 'levels'. All Materia start off at level 1, but can be increased to their max. level. The more level stars a Materia has, the stronger and more useful it becomes. To gain a star level, you have to gain a certain number of Ability Points, just like raising levels or learning Esper magic (in FF3). However, only Materia that you have equipped earn AP. Luckily, that Materia has the same number of points no matter who uses it. For example, let's say Cloud keeps the Summon Chocobo materia equipped for a long time, and manages to raise it to level 2. If Barret, who's never worn that Materia before, equips it, he can also use it at level 2 strength. When you do 'master' a Materia (by gaining all its' levels), you will instantly get another Materia of the same type! Even though it will begin at level 1 (i.e. unused), this means that you can have as many Ultima or Summon Bahamut materia as you want (for example), providing you max out the ones you already have beforehand. Be sure to sell off Materia that you don't need; if you have a full Materia list with no empty places and you master a materia that you have equipped, it will appear in a random location on the list, permanently erasing the Materia that was in it's place (guess the programmers at Square never bothered to check that out, did they?)

You'll want to be careful if you have more than one of the same Materia, because you have to raise them seperately. And there's no point in giving two of the same Materia to the same person! Try to figure out what Materia works best with which person (i.e. give the MAX MP Plus Materia to a good magic-user, and give the Deathblow materia to a character with low normal attack power). Also, take note of the way the holders look; if they don't have silver dots in them (like this: O=O or just O), then you can still equip Materia, but you can't level-up them since none of the AP you gain in battles will be distributed to the Materia in that weapon or item. The tradeoff is that such equipment is usually very strong.