Burning Crusade
Vargoth was the leader of the mages of the Kirin Tor that went to Netherstorm and founded Kirin'Var Village. After surviving the attack of Kael'thas Sunstrider and his blood elves that killed all people in the village except himself, he was locked up in a magical way in the The Violet Tower and guarded by Ar'kelos.
Wrath of the Lich King
Vargoth can be found in Archmage Vargoth's Retreat, a room in the Violet Citadel of Dalaran inaccessible except via a book known as
The Schools of Arcane Magic - Mastery, the quest reward from the achievement
Higher Learning. Vargoth will give you a Kirin Tor Familiar non-combat pet.