Crisis Core Materia Fusion

In the beginning of Chapter 3, you will get the ability to fuse Materia together. This can create better Materia, with higher stats, or completely different Materia. This is the only way to get Zack's stats maxed out.
With the completion of Mission 7-2-1 after chapter 5, you will get the ability to add Items and Accessories into the mix.
There are three important things to consider when fusing Materia together: Materia Rank, Fusion Class, and Fusion rank.
Each Materia in Crisis Core has a class and a rank. This is data that is not seen while playing the game. But it is vital to getting the hang of Materia Fusion.
First the class of Materia. This is what the Materia would be classified. An example class would be the fire class. This would include Fire, Fira, and Firaga.
The rank is is the level of the Materia in the overall system. An example would be a Fire Materia has a rank of 1, and a Costly Punch has a rank of 8. I think of rank as a Materia classes power. The more powerful the Materia, the higher the rank is. The higher ranked Materia will normally become the base of the fusion. For example, if you fused a Jump (rank 1) and a Costly Punch (rank 8) then the Costly punch will end up being the base for the fusion.
Now if the Materia holds the same rank, the higher level Materia will become the base. Say you decided to fuse a Costly Punch level 3, and a Ultima level 5, Ultima will be the base since both are rank 5.
Below is a list of the Materia classes, and the ranking Materia found within. This should be the beginning process for all Materia fusion.

Class	Rank	Class	Rank
Fire	Fire (1) Fira (3) Firaga (5)	Ice	Blizzard (1) Blizzara (3) Blizzaga (5)
Lightning	Thunder (1) Thundara (3) Thundaga (5)	Heal	Cure (1) Cura (2) Curaga (4) Full Cure (6) Regen (3)
Defensive	Barrier (2) MBarrier (3) Wall (7) Elemental Ward (5)	Status Defense	Esuna (1) Dispel (2) Status Ward (4)
Drain Magic	Drain (2) Drainra (5) Drainga (7) Osmose (3) Osmoga (6)	Status Magic	Poison (2) Silence (2) Stop (4) Death (5)
Status Fire	Dark Fire (1) Dark Fira (3) Dark Firaga (5) Hell Firaga (7)	Status Ice	Dark Blizzard (1) Dark Blizzara (3) Dark Blizzaga (5) Hell Blizzaga (7)
Status Thunder	Dark Thunder (1) Dark Thundara (3) Dark Thundaga (5) Hell Thundaga (7)	Gravity	Gravity (2) Graviga (4) Quake (7) Darkness (6)
Ultimate	Tri-Thundaga (3) Tri-Fire (4) Electric Shock (5) Flare (6) Energy (7) Ultima (8)	Speed Sword	Jump (1) High Jump (5) Assault Twister (3) Assault Twister+ (7)
Status Speed Sword	Poison Aerial (3) Silence Aerial (5) Death Jump (6) Poison Twister (2) Stop Twister (4) Death Twister (7) Status Strike (8)	Sword Skill	Power Attack (1) Vital Slash (3) Exploder Blade (6) Blast Wave (5) Elemental Strike (7)
Status Sword Skill	Poison Blade (1) Silence Blade (2) Stop Blade (4) Death Blade (5) Dispel Blade (7)	Fire Sword	Fire Blade (1) Fira Blade (3) Firaga Blade (5)
Ice Sword	Blizzard Blade (1) Blizzara Blade (3) Blizzaga Blade (5)	Thunder Sword	Thunder Blade (1) Thundara Blade (3) Thundaga Blade (5)
Drain Sword	Drain Blade (2) Power Drain (5) Aerial Drain (8) Osmose Blade (3) Power Osmose (6)	Item	Steal (2) Mug (6) Gil Toss (8) Smart Consumer (4)
Punch	Goblin Punch (1) Iron Fist (2) Magical Punch (4) Hammer Punch (6) Costly Punch (8)	HP	HP Up (1) HP Up+ (3) HP Up++ (5)
MP	MP Up (1) MP Up+ (3) MP Up++ (5)	AP	AP Up (1) AP Up+ (3) AP Up++ (5)
Str	ATK Up (1) ATK Up+(3) ATK Up++(5)	Vit	VIT Up (1) VIT Up+ (3) VIT Up++ (5)
Mag	MAG Up (1) MAG Up+ (3) MAG Up++ (5)	Spr	SPR Up (1) SPR Up+ (3) SPR Up++ (5)
SP Turbo	SP Turbo Magic (4) SP Turbo Attack (5) SP Turbo (6) SP Barrier (7) SP Master (8)	Other	Libra (1) Dash (3) Dualcast (8) DMW (8)

Fusion Class

Once you have determined the base of the Materia, you will then need to determine the class of the newly fused Materia.
To find the class of the new Materia, check the table below. The column on the left serves as the class for the base Materia. Next, you need to locate the non-base Materia on the header on the top of the table. The place where the two Materia's connect is the class of the newly fused Materia.
The classes of the old Materia's are no longer valid, once the fusion is complete.
The Fusion Class Table is located HERE. It is a very long table, but I have made images of the tables, for easier viewing and saving to your PC

Fusion Rank & Fussion Results

As it is with the Fusion Class, the Fusion Rank is not always the same as the base Materia's rank. It might serve you as the starting point in the fusion, but there are several things that can change it.
-If the levels of both materia is 1-4, the rank of the new materia is equal to the base Materia.
-If one of the Materia is mastered, add a +1 to the new rank. If they are both mastered (This is a good thing to actually do) add a +2 to the new rank. An example of both would be: You take a Thunder Materia (rank 1) and fuse it with a mastered Blizzara (rank 3), your new rank will actually be rank 4.
If you take a mastered Mbarrier (rank 3) and a mastered Drainga (rank 5), you will actually get a rank of 7. It sounds confusing, I know, but once you get the gist of it, it is simple as a walk in the park.
-In chapter 5, when you complete Mission 7-2-1, you will be given the Item Fusion Tome. This allows items and accessories from your inventory to be fused with the Materia.
*note* Not all items or accessories can be fused. All Key items, summons, and shop cards cannot fuse with items. Most unique accessories cannot be fused.
Items that have a rank are Phoenix Down (4), and Elixir (3). The rest of the items are without a rank. Accessory ranks can be found in the Accessories section.
Using items in fusion can boost or change the fusion rank. If the item and one of the Materia being fused has the same attribute bonus, the item will boost the new bonus. If you fuse an Assault twister with the ATCK bonus and a Power Wrist that shares the ATCK, you will get a higher attack bonus. You need a certain amount of the item to make the bonus increase though. The number of items can also be seen in the Accessory and Items sections.
If the rank of the item/accessory is higher than the base Materia's rank, it then becomes the base rank. The rank of the Materia will be discarded. That said, all the bonuses of the Mastered Materia still go into the fusion, they will just be added to the item/accessory rank instead.

Finished Product

When you combine the Fusion Class and the Fusion Rank, you can then determine what your new Materia will be. In the table located HERE, you can see where the rank and class intersect to get your new Materia. SP is then consumed and all Materia and items used in the fusion are destroyed. You then get the fresh new Materia to use. Remember, that you do have the chance to see the new Materia, and thus back out of the fusion, before you accept the fusion. This is actually good, since not always do you hit it right. Also there are items that can change the attribute of the Materia. These are:

Item Name	Attribute change
Fat Chocobo Feather	Changes attribute bonus to HP
Lunar Harp	Changes attribute bonus to MP
Zeo Nut	Changes attribute bonus to AP
Hero Drink	Changes attribute bonus to ATK
Adamantite	Changes attribute bonus to VIT
Dark Matter	Changes attribute bonus to MAG
Mythril	Changes attribute bonus to SPR
Gysahl Greens	Changes attribute bonus to LCK

With this little bit of information, you should have no problem getting Zack's stats to your liking. Just remember to always save before fusing. This way if there is a mistake made, you do not lose out on anything. Try it out, and have fun experimenting.