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There are just the six spell books, plus cantrip, spell, and megaspell books available in the game. Here, we first just list out all types of books. They can be acquired through fighting enemies, opening chests, in bookshelves or in plain shelves. They can even simply be lying on the dungeon floor. Better books like Spell and MegaSpell tend to be found in magic chests more often.
Here, when a spell is at the spell level in the left column, it needs to be cast [the number in the right column] times. That is, the number in the right column represents how many times a spell book must be used in order to level that spell up.
There's two other ways to raise you magic levels. Option one is to obtain Wisdom Nuts, which level up a random -lower- leveled spell by one. Before using these, be sure to level up your lowest leveled spells to the next level; that way the Wisdom Nut is a bit more effective, saving you a few more spell books. You don't want to waste a Wisdom Nut when you only needed to use just one spell book.
The best way to level up spells is through the use of Mystery Tags. They raise ALL magic levels by one and are the main way to raise all of chocobo's spell levels to 99. These tags are very rare and for the most part are only found in Shiroma's Bonus Dungeon at the end of the game. They are only found in magic spell chests and are very rare. Another way to obtain them is to get lucky and have a Dark Bahamut, a dragon enemy in the dragon floors of the Final Dungeon (Glass Goth Z Dungeon.) For some reason, in Mog's Bonus Dungeon, Mog can't steal Mystery Tags. He steals a "blank" item which should be the Mystery Tag, but you don't obtain one.
Once you hit level 99, the "next level" number is still 20, but when you reduce that number to 0, it resets to 20 and the level stays at 99. For those of you curious, spells at level 99 do roughly 800 - 1100 damage to an enemy, and as much as 1500 to an enemy weak to some element. You can hit as much as 1700 by standing on a magic UP floor tile, while casting a spell on an element-weak enemy. Wow! That's good stuff! (6 - 14 Thunder Books take care of Omega!)
Note: With the exception of Power UP, all cantrips have a slight chance of failure, and this will cause self-inflicting damage.
Note: All spell books have a more-than-slight chance of failure, causing damage to Chocobo.
Note: All megaspells have a pretty good chance of failure, causing moderate damage to Chocobo.