There are five type materia each type has different function and they were the most important in FFVII game, If you want to finish the game 100% you must use materia to it's maximum level.

	Independent Materia
	Support Materia
	Command Materia
	Magic Materia
	Summon Materia

Materia have AP (Ability Points), but not all of them have. There are few materia don't have AP so you don't need to increase the materia level. The AP grows from the weapon or armour your character is using Some weapons and armour have NO-GROWTH and I recommend you not use them. You should aim to use weapon and armour with good growth I.E. Clouds Apocalypse has triple growth so at the end of fights when you get AP it will be tripled. It will only triple the materia on the weapon/armour with the triple growth. Here is a list of where to get materia. In the effect I also suggest what enemies to use it on.

Independent Materia

Materia Name	Function	Location
Cover	Cover others members when getting attacked	Garden near Aeris house
Chocobo Lure	Catching Chocobo	Buy from Chocobo Billy
Long Range Attack	Can be in the back row and still attack for the same damage as if you were in the front row	Climb Vines is Mythril Cave
Counter Attack	Counter enemy attack	After Defeating materia keeper in Nibelheim mountain
Enemy Lure	Increase chance of fighting enemies	250 BP at Battle Square in Golden Saucer
Speed Plus	Increase speed	4000 BP at Batle Square in Golden Saucer
MP Plus	Increase Your MP status	Cosmo Canyon
HP Plus	Increase your HP status	Cosmo Canyon
Luck Plus	Increase your Luck status	Temple Of the ancient
Magic Plus	Increase your magic status	Corral Valley Cave
Pre-emptive	Better chance of attacking first	Golden Saucer
EXP Plus	Gain more EXP on battles, 2x on level 2	2.000 GP at wonder square in Golden Saucer
Enemy Away	Less chace of fighting enemies	Chocobo Racing
HP<->MP	Switch HP to MP and MP to HP	Cave North of North Corel
Mega all	All command will be used in everything. Ie Slash all, heal all and use magic on all players or enemies	Final Dungeon
Underwater	Breath in water while defeating emerald weapon	Kalm Traveler, You must Give him the "Guide Book" First klick here to see it Secret

Support Materia

Materia Name	Function	Location
All Materia	All target will be hit with the materia it's connected to. Ie with restore it will restore all your party and with lightning it will hit all enemies	Fort Condor (Disc 2-3 only), Sector 7 Slums, Shinra Building - Floor 68, Cargo Ship (near Yuffie), Mt. Nibel, Great Glacier.
MP Turbo	Increase in MP and Effectiveness, magic and summons require more MP but are much better	Ancient Temple
MP Absorb	Gain 1/100th of MP that you give in damage. Put it with a magic or summon materia that takes off a lot of MP	Chest in the Item Shop in Wutai (you must complete Yuffie's sub-quest first)
Counter	Betters the chance of your party to use there command	The final dungeon (look in the patch of shiny light in the stone pit area)
Added Cut	When you use the materia connected to the added cut materia you will also make a physical attack after	Located on the second screen of the 'switching path' of the mountain crossroads at the Great Glacier
Added Effect	Can make a status change when you attack	Cosmo Canyon - the Gi Tribe cave
Elemental	Put it on your armour attached to another materia. IE 'fire' and you will recieve less damage for fire and with a high level elemental you can absorb HP	Shinra Building - Floor 62, Mt. Corel, Nibelheim (it's in Tifa's piano)
Steal As well	After use the materia attached to 'Steal As Well' materia you will also make a steal attempt	Wutai village - extinguish the large fire-pit in the cave found in the Dachao Statue area
Final Attack	When you die you can make an attack of some sort with the connected materia	Win this by completing the 'special battle' being offered at the Gold Saucer's Battle Square
Magic Counter	Counter Attack with magic or summon	Win this at the Gold Saucer's Chocobo Square
Sneak Attack	You can have the first attack of the battle. IE cast a summon before anything else happens in the battle. Just connect it to the magic/summon you would like to cast first	Win at the Gold Saucer's Chocobo Square
Quadra Magic	Use magic four times. IE cast ultima magic once and it'll automatically cast 4x	In the cave at the end of the chain of peninsulas near Mideel village
HP Absorb	Gain 1/10th of HP that you give in damage. Put it with a magic or summon materia that takes off a lot of HP	In the cave at the end of the chain of peninsulas near Mideel village

Command Materia

Materia Name	Function	Location
Sense	Let you to see enemies statistic	Kalm town, Upper Junon, Midgar City - Playground outside of the Wall Market
Steal	Steal Item from enemies	Midgar City - Sewers (before/after the fight with Aps), Kalm town
Deathblow	Make double HP attack, not every times succeed	Fort Condor, Rocket Town, Jungle area near Gongaga village
Throw	Throw a weapon you are not using at the enemy or throw Gil at them for the amount og HP you want to take off	Condor Fort (Disc 2-3 only), Rocket Town (Disc 2-3 only) (Also comes with Yuffie)
Manipulate	Manipulate enemy, and control them	Fort Condor (Disc 2-3 only), Rocket Town (Disc 2-3 only) (Also comes with Cait Sith)
Morph	Turn enemy to item when you kill them	Temple of the Ancients
Enemy skill	Learn enemy skill, toe see the enemy skill list got to menu enemy skill list	Shinra Building - Floor 67, Upper Junon (in the Respectable Inn), Forgotten Capital, Chocobo Sage's house (Talk to the Green Chocobo and one will just appear)
Mime	Do the same thing that the last person did. Mime them	In the cave on the Western Continent. A Green/Black/Gold Chocobo is needed. Near Wutai
Double Cut	Attack x2 or x4 depending on the level	In the wrecked plane under the water. Use Submarine to get to it
Slash all	Attack all opponents when you attack or Flash which kills all enemies in front of you	Ancient Forest
W-magic	Cast two magic spells in one go	In Northern Crator - I'm going to tell you exactly what to do from the place you meet up with your characters and there are two paths. You can go right or down. Go down here. Then you will be at the top of the screen. There are another two paths. Go in the top one. You should be in a lake like area. Make you way through the screen by going under the water etc. Then keep going through the next screen. Now you should be out in the open. There should be green shubs around. Search around these scrubs it's about in the middle of the screen, the color of it is purple even though it's a command materia.
W-Summon	Cast two summon spells in one go	Buy from Battle Square in Golden Saucer. Battle points needed 65000
W-item	Use two items in the one go	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 do all materia command. Mime, 2x cut, throw, etc.	You can kill the Emerald Weapon and get Master Command off the Kalm Traveller or goto Cosmo Canyon with the 8 Mastered Command Materia listed. Only the 8

Magic Materia

Materia Name	Level	Function	Location
Ice	Ice 1 Ice 2 Ice 3	Cast Ice spell, Use it on hot enemies	Wall Market, Costa Del Sol, Mideel, Fort Condor (Also comes with Cloud)
Lightning	Bolt 1 Bolt 2 Bolt 3	Cast Lightning, Use it on Mechanical enemies	Wall Market, Costa Del Sol, Mideel, Fort Condor (Also comes with Cloud)
Fire	Fire 1 Fire 2 Fire 3	Cast fire magic, use it on cold enemies	Wall Market, Costa Del Sol, Fort Condor, Mideel (Also comes with RED XIII)
Restore	Cure 1 Cure 2 Regen Cure 3	Heal your member party	Midgar City - Sector 5 Slums, Wall Market, Mideel, Fort Condor, Costa Del Sol, Mako Reactor No. 1
Poison	Bio 1 Bio 2 Bio 3	Cast poison spell, Use it on living creatures	Kalm town, Costa Del Sol, Shinra Building - Floor 68
Earth	Quake 1 Quake 2 Quake 3	Earth Damage, Ground enemies	Kalm town, Costa Del Sol
Heal	Poisona Esuna	Heal all abnormal status, including poison	Kalm town, Gongaga village, Upper Junon
Revive	Life 1 Life 2	Revive your allies, More hitpoints for higher level	Upper Junon, Gongaga village, Costa Del Sol
Seal	Sleep 1 Sleep 2	Make enemies sleep and silence	Upper Junon, Costa Del Sol
Transform	Mini Toad Confu	Transform your enemies to mini or Frog	North Corel, Cosmo Canyon, Gongaga village, Mideel, Mt. Corel (Also comes with Cait Sith)
Mistify	Confu Beserk	Confusion and beserk	Gongaga village, Cosmo Canyon
Time	Haste Slow Stop	Haste your self/allies, Slow, Stop your enemies	Gongaga village, Rocket Town
Gravity	Demi 1 Demi 2 Demi 3	Gravity Damage, Use it on Fly enemies	Cosmo Canyon; it appears after you kill Gi Nattak in the Gi Tribe Cave
Destruct	DeBarrier DeSpell Death	Destruct enemies barrier and magic barrier	From Sephiroth he will throw it at you (Shrina Mansion), Fort Condor and Mideel
Barrier	Barrier M-Barrier Wall	Cast physical attack barrier, magic barrier, and two of them on Your allies	Rocket Town
Exit	Escape Remove	Escape from fighting	Rocket Town
Comet	Comet 1 Comet 2	Cast comet spell, Physical Damage	Forgotten Capital - In one of the little house things
Fullcure	Fullcure	Cast Full Cure HP on your ally, level 2 only	In Cosmo Canyon. The last shop, climb up the rope and go into the back room and it will be there waiting for you to pick it up.
Contain	Freeze Break Tornado Flare	Ice, Earth, Physical and Fire Damage - Depending on the Level	In Mideel from the white chocobo. Give it Mimett greens and scratch it's ear
Ultima	Ultima	Extreme Magic attack, level 2 only	North Corel - After saving the train you get it off a little boy at North Corel. If you don't save the train you can buy it for 50000 Gil.
Shield	Shield	Became invisible for a while	In Northern crator. In the swampy part, go into a few parts of water and you will eventually come up at it
Master Magic	All Magic spells	Use all magic spells. you need the MP for it though. No AP on Master Materia	Get it after you kill the Emerald Weapon, go to Kalm town with the Earth Harp you get for beating the Emerald Weapon. Go to Cosmo Canyon with all the Mastered Magic Materia and change it to a Master Magic by going to the Huge Magic Materia

Summon Materia

Materia Name	Effect	Location
Choco/Mog	Physical Damage	Talk to chocobo at the chocobo Billy's farm
Shiva	Ice Damage	Get from priscilla at Junon after you save her
Ifrit	Cause fire damage	After fighting Jenova birth on the cargo ship to Costa Del Sol
Ramuh	Lightning damage	At the correl prison, when you want to race chocobo
Titan	Earth Damage	At the meltdown reactor near Gongaga town
Leviathan	Water Damage	After defeating 5 gods in pagoda at wutai, You must use Yuffie
Kjata	Fire, Ice, Lightning, earth damage	Sleeping forest, it's moving along the screen
Bahamut	Non element damage, Mega flare attack	After Killing the red dragon at the ancient temple
Alexander	Holly damage	at great glacier after defeating snow, woman in purple dress in the cave
Neo Bahamut	Non element Damage, Giga flare attack	Near the Whirlwind Maze search the buttom of the screen
Odin	Cause Physical attack, sometimes instant death (but not work with the boses)	At the shinra mansion, Nibelheim town. It was in the safe after you kill the "big guy"
Phoenix	Fire damage 2x, and life for the death allies	After defending the fort Condor
Hades	Causes Non-Element Damage, and randomly inflicts Confuse, Frog, Minimum, Paralyze, Silence, Sleep, and Slow	Lying near the wrecked helicopter in the storage area of the sunken 'Gelnika' prototype aircraft
Bahamut Zero	Non element attack, Terra flare	Gather all the huge materia, there are 5, but you can collect 4 of them. Each huge materia has same color as command, support, summon, independent, magic and place them at Bugenhagen's House
Typoon	Cause Wind/typoon damage	Lying on the large tree branch in the Frog Forest/ancient forest
Knights Of the Round (KOR)	Various attacked to enemies, elemet, non element, and physical attack. 13 hits in all (each hit cause damage 9999)	Use a Gold Chocobo to get to Round Island in the northeast corner of the map.
Master Summon	The same as other Master Materia. You can cast all of them as many as you want not depend on the AP level.	Take all the Mastered Materia to Cosmo Canyon and go to the 'Red Huge Materia'. Or You can kill the Emerald weapon and take the 'Earth Harp' you get off him to the Kalm Traveller

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All Materia List I gathered from My experience Playing FFVII and -=[Final Fantasy VII World]=- thanks for the materia information too.