Here are the 5 types of materia in ff7:

Independent Materia
Support Materia
Command Materia
Magic Materia
Summon Materia
 

Almost all of the materia in the game has AP (ability points).  After each battle you earn AP and each materia has it's own requirements to move up a level.  After materia has moved up it's last level it gets mastered and when materia masters you get another one of the type you mastered in the first level.  Some weapons and armor have different growth rates (most are normal growth) some of the good weapons of the game like Cloud's Apocalypse sword have triple growth, which means that after each battle you get triple the AP for the materia equipped in that weapon.  For example if you earned 5 AP after a battle the materia equipped in that weapon would actually get 15 AP (this comes in very handy when you fight the pots in the final dungeon, they give you a crapload of EXP and AP).
 
 
 
 
MAGIC MATERIA  Back to Top
Materia Name What it does Where it's found or bought
Fire Fire Damage-works better on cold enemies Wall Market, Costa Del Sol, Fort Condor, Mideel (also comes with RED XIII)
Ice Ice Damage-works better on fire enemies Wall Market, Costa Del Sol, Fort Condor, Mideel (also comes with Cloud)
Lightning Lightning Damage-mechanical enemies Wall Market, Costa Del Sol, Fort Condor, Mideel (also comes with Cloud)
Earth Earth Damage-ground enemies Kalm Town, Costa Del Sol
Poison Poison Damage-living enemies Kalm Town, Costa Del Sol, Shinra building 68th floor
Gravity Gravity Damage Cosmo Canyon; it appears after you kill Gi Nattak in the Gi tribe cave
Comet Physical Damage from a comet Forgotten Capital in one of the little buildings
Contain Ice, Earth, Physical Damage and Fire Damage depending on the level The white chocobo in Mideel, scratch behind it's ear.
Ultima Non element damage to all enemies-it has to be moved up a level before you can use it North Corel-If you save the town you get it for free if you don't it costs 50,000 gil
Restore Restores HP depending on the level (level 3 Regen Status) Midgar City-Sector 5 slums, Wall Market, Mideel, Fort Condor, Costa Del Sol, Mako Reactor #1
Full Cure  Fully restores HP-level 2 only the last shop in Cosmo Canyon, up the rope in the back room
Heal Heals poison etc. Kalm Town, Gongaga Village, Costa Del Sol
Revive Revives a player, amount of HP depending on level (the higher the better) Upper Junon, Gongaga Village, Costa Del Sol
Seal Gives enemy Sleep and Silence Upper Junon, Costa Del Sol
Mystify Causes confusion and beserk Gongaga Village, Cosmo Canyon
Transform causes small and frog North Corel, Cosmo Canyon, Gongaga Village, Mideel, Mt. Corel (comes with Cait Sith)
Exit Level 1 you can escape from a battle- Level 2 you can remove an ememy from a battle Rocket Town
Time Haste, Slow, Stop Gongaga Village, Rocket Town
Barrier Barrier, Magic Barrier, Reflect, Wall Rocket Town
Shield An allie becomes invinsible for a short period of time Northern Crater
Destruct Removes Barrier and other Defenses Shinra Mansion (Sephiroth throws it at you), Fort Condor, Mideel
Master Magic Cast all the magic from one materia, you need the MP though, NO AP Kill Emerald Weapon go to Kalm Town with the earth harp you get from beating Emerald Weapon or go to Cosmo Canyon with all the mastered magic materia and change it to a master magic by going to the huge magic materia

 
 
 
 
COMMAND MATERIA  Back to Top
Materia Name What it does Where it's found or bought
Sense Shows you enemy statistics Kalm Town, Upper Junon, Midgar City-by the entrance to the playground
Steal A chance to steal or mug an enemy Midgar City-in the sewers before or after the fight
Throw Throw a weapon (very effective but it costs quite a bit to buy all the items you need) Fort Condor (Disc 2-3 only), Rocket Town (Disc 2-3 only), also comes with Yuffie
Deathblow Attack for twice the regular HP (doesn't always work) Fort Condor, Rocket Town, Jungle by the Gongaga Village
Manipulate Control and Command one enemy Fort Condor (Disc 2-3 only), Rocket Town (Disc 2-3 only), Also comes with Cait Sith
Morph Takes out approximately 1/8 the HP but if you kill the enemy with it you turn them into an item Temple of the Ancients
Enemy Skill When attacked by certain enemys you learn certain skills Shinra Building-67th floor, Upper Junon (in the inn), Forgotten Capital, Chocobo Sage's house (talk to his chocobo and he'll spit it out for you)
Mime Perform the same action as the last person (mime them) The cave on the western continent near Wutai (a Green/Black/Gold chocobo is needed)
Double Cut Attakc 2x for level 1 and attack 4x for level 2 The wrecked plane in the ocean (you have to use the submarine to get to it)
Slash All Attack all enemies in level 1 and flash all enemies in level 2 (the flash is handy because it instantly kills all the enemies, it helps to get through many battles easily if you equip it with your 1st character) Ancient Forest
W-Magic Cast two magic spells in one turn  Northern Crater
W-Summon Cast two summon spells in one turn Buy in battle square in golden saucer for 65,000 BP
W-Item Use two items in one turn (you can also use the copy item trick with this materia) The southernmost end of the rail track in the subways below Midgar City (during the raid at the end of disc 2)
Master Command You can use Deathblow, Coin, Manipulate, Morph, Mime, Sense, Steal, and Throw in your goes Kill the Emerald Weapon and get the master command off the Kalm traveler or go to Cosmo Canyon with the 8 mastered command materia listed (only the 8)

 
 
 
 
INDEPENDENT MATERIA  Back to Top
Materia Name What it does Where it's found or bought
HP Plus Increase HP by 10-50% depending on the level Cosmo Canyon, Mideel Village
MP Plus Increase MP by 10-50% depending on the level Cosmo Canyon, Mideel Village
HP<->MP Reverses Max HP and Max MP The cave on the peninsula near Mt. Corel
Luck Plus Increase your luck by 10-50% depending on the level Temple of the Ancients 
Magic Plus Increase you magic score by 10-50% depending on the level Cave area past Forgotten Capital, search near the bottom of the long ladder to the left
Speed Plus Increase your speed by 10-50% depending on the level  Buy at the Battle Square in the Golden Saucer
Gil Plus Earn more Gil after battles depending on the level Buy at the Battle Square in the Golden Saucer
EXP Plus Earn more EXP after battles depending on the level  Buy at the Battle Square in the Golden Saucer
Enemy Away Don't encounter as many enemies Win racing in the Chocobo square at the Golden Saucer
Enemy Lure Encounter more enemies  Win racing in the Chocobo square at the Golden Saucer
Chocobo Lure Encounter chocobs while moving on their tracks Buy from Chocobo Billy at the Chocobo Barn or find near the outside chocobo pen's right corner
Pre-Emptive Increase rate of Pre-Emptive attacks Buy at the Golden Saucer's Battle Square
Long Range Attack for same damage in back row as in front row Mythril Mine on the ledge above the mine
Cover A chance to cover another allie if they are attacked depending on the level  Wall Market, Sector 6 Slums (the garden near Aeris's house) 
Counter Attack Attack when you get attacked rate depending on the level Mt. Nibel (after destroying the materia keeper), or win as prize in the Gold Saucer's Chocobo Square
Mega All All command will be used with everything The Final Dungeon floating in the Geyser you have to press O while jumping to get it
Underwater You won't drown when fighting the Emerald Weapon as the time limit decreases Kalm Town from the traveller if you give him the Guide Book

 
 
 
SUPPORT MATERIA  Back to Top
Materia Name What it does Where it's found or bought
HP Absorb Gain 1/10th of HP you dish out, good idea to put it with KOR or another good summon to get a lot of HP The Final Dungeon
MP Absorb Gain 1/100th of MP that you dish out in damage, another good one to put with KOR Wutai, the chest in the item shop after you complet Yuffie's subquest
MP Turbo Increase in power of paired magic with more MP but it's worth it Ancient Temple
All All powers with connected materia ie all connected to restore will heal all allies Fort Condor (disc 2-3 only), Sector 7 slums, Shinra Building 68th floor, Cargo Ship (near Yuffie), Mt. Nibel, Great Glacier
Quadra Magic Cast the connected materia 4 times The cave near Mideel Village
Sneak Attack You can start the battle with anything before they do The Gold Saucer's chocobo square
Magic Counter Counter attack with paired magic or summon The Gold Saucer's chocobo square
Counter Betters the chance of your party to use their command  The Final Dungeon (the patch of shiny light in the stone pit area)
Final Attack You have the power to do something right before you die (good idea to connect this with Phoenix Summon to bring you back to life) Win the special battle at the Battle Square in the Gold Saucer
Added Cut When you use connected materia you will also attack The second screen of the switching path of the mountain crossroads at the great glacier
Steal As Well When you use the connected materia you will also attempt to steal Wutai in the Duchao Statue by putting out the flame with the levithian scales
Added Effect Make a status change when you attack Cosmo Canyon in the Gi cave
Elemental Put it in armor attached to fire or something similar to be protected from it Shinra Building 62nd floor, Mt. Corel, Nibelheim (Tifa's Piano)

 
 
 
SUMMON MATERIA  Back to Top
Materia Name What it does Where it's found or bought
Choco/Mog Wind Damage Watch the chocobos dance at the chocobo farm
Shiva Ice Damage Priscilla in Junon
Ifrit Fire Damage After killing Jenova Birth on the cargo ship make sure you get it before you get off
Ramuh Lightning Damage The back of the jockey room in Corel Prision
Titan Earth Damage The right side of the Meltdown Reactor in Gongaga Village check around to find
Leviathian Water Damage Beat all the enemies in the pagoda with Yuffie
Kjata Fire, Ice, and Lightening damage all in one shot The second screen in the sleeping forest 
Bahamut Non-Elemantal Damage You get it after killing the red dragon in the Temple of the Ancients
Alexander Holy-Elemental Damage Touch the hot springs then go kill the woman
Neo Bahanut Non-Elemental Damage x2 The bottom of the screen near the whirlwind maze
Odin Instant Death if possible or Physical Damage The safe in Nibelheim after you kill the monster
Phoenix Life2 on all allies and Fire Damage x2 Win the "mini" battle at Fort Condor
Hades Non-Elemental Damage and randomly conflicts Confuse, Frog, Minimum, Paralyze, Silence, Sleep, and Slow The Sunken Aircraft in the bottom of the ocean
Bahamut ZERO Non-Elemental Damage x3 Have Bahamut and Neo Bahamut and take it to Cosmo Canyon to the Blue Huge Materia
Typhoon Instant Kill/Non-Elemental Damage The large tree branch in Frog Forest
KOR (Knights of Round) 13 Various attacks to all enemies (the best summon materia in the game) The cave in the round island on the northeast corner of the map (it's not on the map) you also have to have a gold chocobo to get it
Master Summon Just like all the other master materias you can cast all of them as you want to Take all the mastered materia to Cosmo Canyon and go to the Red Huge Materia
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