Confront the King

Overview
Faction: Mages Guild

Quest giver: Hannibal Traven at the Imperial City Arcane University

Prerequisites: Completion of Ambush

Reward: Rank Arch-Mage (technically, you already are arch-mage after Traven sacrifices himself, but you are officially recognized by Raminus Polus after you return.), Arch-Mage Robes, and the staff of worms.

Background Information
Hannibal Traven gives you your final task of killing Mannimarco, the King of Worms.

Quest Details
Traven promotes you to Arch-Mage, sacrifices himself and puts his own soul into the Colossal Black Soul Gem. Search his body and take his key and the Soul Gem. Head to Echo Cave, where the King of Worms can be found.

Outside the cave, a guard will be waiting. He gives a lovely speech and states he will die protecting the key, and proceeds to attack you. Oblige him, take his key, and enter the cave. Work your way through the cave and the many Necromancers until you get to the bottom level where you encounter Mannimarco the King of Worms. He also has a speech for you, in which he recognizes the growing annoyance you are to necromancers, and then proceeds to use his enthrall spell on you (this is the same spell that turned poor Mucianus Allias into a worm thrall). However the presence of the colossal black soul gem in your inventory negates this effect. Thus robbed of his critical weapon, you can finish him off. He is twenty levels above your own, with a range of nasty spells and scrolls, not to mention he's standing next to a lever that activates a claw trap. Kill him and the job is done. He carries the Staff of Worms, which allows you to reanimate the dead.

Head back to the University, Raminus Polus will acknowledge you as Arch-Mage and provide guidance on what you should do next. You will receive a new robe/hood and other bonuses. You can use the offices/quarters as your own. You can also enlist two apprentices (there's a few that wander the University) to follow you and fight. However, if you kill them, you will be expelled from the guild and forced to collect ingredients for readmission, unlike the generic Dark Brotherhood murderers that follow you. There's also an Enchanted chest, which multiplies any ingredient you put in it after 24 hours (excluding Nirnroot and ingredients from the Shivering Isles). Speak to Raminus Polus about Alchemy Acquisitions after being made Arch-Mage for a short quest regarding the chest.

This is the final quest of the Mages Guild. You can go many ways from here, such as try to destroy the remnants of the necromancer threat. Keep in mind that all the items previously locked in display cases are no longer considered stolen. In fact the only items still considered 'stealable' are on and around the counter in the room left of where you enter the Anvil Mages Guild.