The Archmage is a member of the Villain League, and is considered to be the Biggest of all Big Bads in Gargyoles. He was a powerful but arrogant and greedy magician. He taught both the Magus and Demona how to use magic, having once been a courtier at Castle Wyvern and he was the first person known to possess the spellbook called the Grimorum Arcanorum.
In 975, the Archmage sent Demona to steal the Phoenix Gate from Princess Elena, while he was still the premier spellcaster in service to Prince Malcolm. Though he did not act openly, he desired the Phoenix Gate to combine with his Grimorum Arcanorum and the Eye of Odin, which would give him ultimate power. In this instance, he failed to retrieve the Phoenix Gate.
The Archmage poisoned Prince Malcolm, the lord of Castle Wyvern in retaliation for his banishment. Three gargoyles, who would later be named Hudson, Goliath and Demona, tracked him to a cave where he had hidden himself in order to retrieve the antidote and save Prince Malcolm. During this encounter, he blinded the future-Hudson in one eye, then seemingly fell to his death when attempting to retrieve the Grimorum.
The Archmage became a far greater threat when he attacked Avalon. Apparently, he had survived his fall into the chasm by traveling back in time and saving himself. By manipulating events, and coercing the Weird Sisters to do his bidding, he managed to obtain the Grimorum Arcanorum, the Phoenix Gate and the Eye of Odin, granting him ultimate power as he had long wished. Using his powers, he rescued himself in the past and then arranged for himself to gain the three items, before his younger self set out to do the same in a predestination paradox.
Having gained his new powers, he aimed to conquer the world, but was informed by his future self the technological advances in the modern world would require him to have base of operations where his enemies could never touch him, Avalon, and thus he laid siege to it and attacked the Avalon Clan that lived there. However, he refused to destroy them immediately because he wanted revenge on Goliath and believed that he was invincible. His hubris allowed the Avalon Clan, with Goliath's help, to mount a counter-attack. Goliath managed to steal the Eye of Odin away from him, and without the Eye, he was unable to control the power of the Grimorum Arcanorum, having previously swallowed it in order to circumvent the law that the book could never enter Avalon, and it destroyed him, turning him to a pile of dust.
According to Greg Weisman, he makes an unseen trip through time either during Avalon Part 2 or 3. That particular trip would be detailed in the unmade spinoff, Timedancer.
Also, he would be a main character in the unmade prequel to Gargoyles, Dark Ages, which would have followed the exploits of the gargoyles of the Wyvern Clan (younger versions of Goliath, Demona, Hudson, Coldstone and others) before the massacre of the clan. It would have revealed more of the Archmage's past, including his alliance with Prince Malcolm, and his double dealings with the gargoyle Iago
Role in the series
The Archmage has not appeared yet in the series. But if he does, Spongebob will have to get Merlin into his team, and quickly!