Although his fiery red fur may make him look like a wild animal, Red XIII's intellect is well above that of most humans.  Not much is known about Red XIII's origin.

He's currently being held captive in Shin-Ra's headquarters where he's forced to participate in their twisted experiments.
Level 1:  Sled Fang-- Red XIII Charges through an opponent causing a large amount of physical damage.  For a while this may be the only long-range attack Red XIII has, so it's sure to come in handy.  However, it'll become obsolete by the time you recieve Blood Fang.  Lunatic High-- A glowing light covers the party and Haste is cast on everyone.  Until you've purchased the "Time" Materia, the Lunatic High should come in handy during major battles.
Level 2:  Blood Fang-- Red XII charges through an opponent causing more physical damage than the Sled Fang attack.  He also gains a small amount of Hit Points and Magic Points.  This attack isn't much different from the Sled Fang attack, but it's for eliminating an opponent and boosting Red XII's MP.  Stardust Ray-- Red XIII's hown summons a cluster of falling stars, which causes severe damage to a group of enemies.  Unless you need the MP boost, stick with the Stardust Ray during fights.  It inflicts considerably more damage to a group or a single enemy than the Blood Fang.
Level 3:  Howling Moon-- The full moon drives Red XIII into a rage, casting Beserk and Haste on him for the remainder of the battle.  This attack has some obvious advantages and disadvantages.  Using this attack, Red XIII can attack quickly, but he can no longer aid the party with magic or any kind of special attack.  Earth Rave-- Red XIII attacks a group of enemies with a series of five elemental attacks.  In the end, the Earth Rave will prove more beneficial than the Howling Moon.  It does a large amount of direct damage without committing Red XIII to a single attack pattern.
Level Four:  Cosmo Memory-- To get Red XIII's Cosmo Memory Limit Break, you must defeat the Lost Number Boss in Shin-Ra Mansion.  This requires opening the safe on the second floor of the house (combination Right 36, Left 10, Right 59, Right 97).  Red XIII summons a hoge ball of fire which explodes, engulfing his opponents in a huge ray of super-heated plasma.