The Red Mage is a job in the Final Fantasy series that possesses the ability to cast both white and black magic. They also get perks like better armor, the ability to wield swords, and such.
You've seen the kind of kid before. They want knowledge, they suck it in like a frilling vortex of epistemology. It's the geek with zits and glasses at the back of your Algebra for really smart people class. It's the tomboy in Chemistry that knows every combustion reaction by heart.
At its core, the life of the Red Mage is the quest to know Everything. It's not enough to know the white magic -- the healing arts, and the left-hand magic -- no, and it's not enough to specialize in black magic. It's not even enough to specialize in magic. They learn the art of fighting, usually with swords, and how to wear armor much heavier than their magi counterparts.
The Red Mage can learn up to 6th level white and black magic. In exchange for knowing both halves of the coin, they lose all the instadeath spells. They can wear medium armor and shields, along with much better weapons than your average mage.
The Red Mage simply knows the union of all the white and black magic you've bought for the character; but with a level 3 restriction on magic of both levels. The Red Mage's master ability, X-Magic, allows the character to cast 2 spells in one turn. Such great power comes at a great price -- 999 Ability Points to snag the skill of the master Red Mage.
For the first time, there are spells that only a Red Mage can cast:
Also, Red Mages get both the white and black enfeebling and enhancing magic, though not all of either. They miss out on the elemental enfeebles -- Frost, Shock, Burn, Choke, Rasp, and Drown -- and White Mages get many of their buffers long before their Red counterparts. Raise is a lv. 37 Red Mage spell, instead of being a lv. 25 White Mage. Also, all the -ra variants (that target the whole party) are forbidden to Red Mages.
The three best subclasses for Red Mage, in no particular order, are White Mage, Black Mage, and Summoner -- though many would dispute the merit of Summoner as a subjob.
One of the more popular Red Mages is, Red Mage, from 8-Bit Theater. For some reason, he's a meta-gamer who knows the PHB, DMG, etc. by heart.