---MAGIC MATERIA---
Auto-Cure. Casts Cure on severely injured allies up to a set number of times. Will not activate if the character does not have enough ATB charges and MP, or the player is controlling the character. (Not quite sure where to put this, as it's one of those AI materia, but it doesn't seem to require you to link it to the Healing materia, so its not Support. And it consumes MP, so it's not Command or Independent...)
Barrier. Allows you to use defensive spells.
Binding. Allows you to use disruptive spells. (b/c a support materia groups this materia in with Poison, Subversion, and Time, I assume this contains various status effect spells -- it could be a reskin of Mystify (confuse, berserk) or Transform (mini, toad) which are both originally found on the West Continent.)
Chakra. Allows you to restore your own HP and cure poison with Chakra. The amount restored is relative to your current HP, and more is restored the lower your HP. (This could also be a Command materia. We've seen Chakra in other FFs as a monk ability, it usually restores HP and MP and doesn't cure poison.)
Cleansing. Allows you to use curative spells. (I assume this is Heal, not Restore, as "cleanse" implies a removal of status effects, and the description of Chakra uses "cure" to describe the removal of the poison status effect. The language around curing and healing is as obfuscated as ever. Anyway, Heal was formerly found in Kalm.)
Fire. Allows you to use fire magic.
Healing. Allows you to use healing spells. (I assume this is Restore, not Heal.)
Ice. Allows you to use ice magic.
Lightning. Allows you to use lightning magic.
Poison. Allows you to use toxin-related spells. (Formerly found in Kalm. Why doesn't the description just say "poison magic"?)
Prayer. Allows you to restore the party's HP with Pray. (No Restore-All? Or, rather, Healing-Magnify? Booo. This might even be a Command materia, depending on whether Pray consumes MP or not.)
Revival. Allows you to use revival spells. (Formerly Revive, found in Junon)
Subversion. Allows you to use subversive spells. (b/c a support materia grouping this materia in with poison, bind, and time, I assume this contains various status effect spells -- it could be a reskin of Mystify (confuse, berserk) or Transform (mini, toad) which are both originally found on the West Continent.)
Time. Allows you to use time magic. (Formerly found in Gongaga.)
Wind. Allows you to use wind magic. (Wow!)
---SUPPORT MATERIA---
AP Up. Increases amount of AP earned for linked materia. (Ooh baby!)
Elemental. Adds the element of the linked materia to your equipment, infusing your attacks with and gaining resistance to that element. When more than one is set, only the first takes effect. Works with fire, ice, lightning, and wind materia. (Looks like weapon/armor placement is irrelevant, you get both)
HP Absorption. Allows you to recover HP when unleashing an attack of the linked materia's type. (Formerly HP Absorb, found during Yuffie's questline.)
Magnify. Allows you to expand the range of spells with the linked materia. To switch back to a single target, press (L1) when selecting a spell. (This functionally replaces the All materia with an AoE version of the linked spell. (sidenote: that's what I did with my ttrpg system!))
MP Absorption. Allows you to recover MP when unleashing an attack of the linked materia's type. (Formerly MP Absorb, found during Yuffie's questline.)
Synergy. Allows you to follow the leader's attack command with an attack from linked materia. Works with fire, ice, lightning, wind, and poison materia. (Another AI control materia, this one's clearly a Support. Could be fun to use, especially with a straight black mage build.)
Warding. Grants resistance to the linked materia's status ailment. Works with poison, time, bind, and subversion materia. (This is just the armor version of Added Effect, as it doesn't appear that weapon/armor placement has any relevance for this or Elemental anymore.)
---COMMAND MATERIA---
Assess. Allows you to use Assess. (This is a reskin of Sense, we've seen it in action during official presentations.)
ATB Boost. Doubles ATB when activated. Cannot be used continuously. Press (L1) + (R1) to activate. (What do they mean by continuously? Is there a recharge on this ability?)
Deadly Dodge. Attack command will do area damage immediately after dodging. (One of those 'not sure if yellow or purple' materia. Since you activate it by dodging, I'm guessing yellow).
Enemy Skill. Allows you to learn certain enemy techniques that you've endured and use them as abilities. These abilities can only be used when the materia is set to your equipment.
Parry. Guards against enemy attacks and allows you to quickly unleash your next move. Hold (R1) and press (cancel) to activate. Deals a small amount of damage.
Refocus. Allows you to use the Refocus limit break. Can only be used once per battle. (This is... a really cool concept)
Steal. Allows you to use Steal.
---INDEPENDENT MATERIA---
ATB Assist. Slightly fills teammates' ATB gauges when ATB commands are used back-to-back.
ATB Stagger. Increases ATB when staggering an enemy.
EXP Up. Increases the amount of EXP you earn in battle. (Formerly EXP Plus, won at Wonder Square)
First Strike. Increases how full the ATB gauge is at the start of battle. (A kind of modified Speed Plus? But nerfed)
Gil Up. Increases the amount of gil you earn in battle. (Formerly Gil Plus, found at Wonder Square)
HP Up. Increases your max HP. The total boost limit is +100% when more than one is equipped. (Formerly HP Plus, found in Cosmo Canyon)
Item Master. Increases the effectiveness of items used in battle. (In other FFs this is usually called "chemist")
Luck Up. Increases your luck. The total boost limit is +100% when more than one is equipped. (Formerly Luck Plus, found at the Temple of the Ancients)
Magic Up. Increases your magic attack power. The total boost limit is +100% when more than one is equipped. (Formerly Magic Plus, found at the Forgotten City)
MP Up. Increases your max MP. The total boost limit is +100% when more than one is equipped. (Formerly MP Plus, found in Cosmo Canyon)
Pedometer. May do something after taking a number of steps with it set. (Eh? Like a cat's bell? What could it be I wonder...?)
Provoke. Automatically uses Provoke to temporarily draw the enemy's attention when teammates are severely injured. Ineffective against powerful enemies. Will not activate if the player is controlling the character. (This seems to be a modified version of Cover, using the new AI)
Steadfast Block. Further decreases enemy damage and fills the ATB gauge faster when guarding. (This is also a kind of nerfed Speed Plus)
Skill Master. Slightly fills the ATB gauge when multiple ATB commands are performed.
---SUMMON MATERIA---
Bahamut. Allows you to summon Bahamut. (Formerly found in the Temple of the Ancients.)
Cactuar. Allows you to summon a cactuar. (new)
Carbuncle. Allows you to summon Carbuncle. (new)
Chocobo & Moogle. Allows you to summon a chocobo and moogle. (Formerly Choco/Mog, found at the chocobo ranch.)
Chocobo Chick. Allows you to summon a chocobo chick. (new)
Fat Chocobo. Allows you to summon a fat chocobo. (Formerly part of Choco/Mog as a rare percentage chance to appear instead.)
Ifrit. Allows you to summon Ifrit. (Formerly found on the cargo ship.)
Leviathan. Allows you to summon Leviathan. (Yuffie confirmed! jk. It was formerly the reward for completing her questline.)
Shiva. Allows you to summon Shiva. (Formerly found in Junon.)