Mages Guild

Dedicated to study and learning, the Mages Guild is the Imperial faction that oversees the training and use of magic in Vvardenfell. This does not sit well with the sorcerous House Telvanni, so you will often find the two at odds with each other. You can join both if that suits your fancy.

Members of factions receive different types of welcomes from members of other factions, depending on how they get along. The formula is (Faction Reaction * 5)*(0.5 +(Faction Rank *0.5)). In plain terms, this means that as you attain higher ranks in your faction, people with negative modifiers will like you less and people with positive modifiers will like you more. This does not mean that everyone will start attacking you on sight, nor does it mean that they are going to fall all over themselves to be helpful. It does, however, modify their initial disposition toward you. This initial disposition will be further modified by your Personality, your overall reputation, your Criminal Status, whether or not you are Diseased, what kinds of favors you have done for the faction you're dealing with, etc. The other person may wind up liking you a lot or not liking you at all, but your faction and rank can impose a serious modifier.

Reactions to Other Factions
Hated Enemy (-3)	Enemy (-2)	Hostile (-1)	Indifferent (0)	Friendly (+1)	Ally (+2)	Beloved Ally (+3)
House Telvanni	Temple Ashlanders Camonna Tong Vampires	House Redoran House Hlaalu Fighters Guild Imperial Legion Thieves Guild	Morag Tong	Imperial Cult		Mages Guild

Advancement within the Mages Guild will depend upon your skill level in three of the following skills:

Alchemy
Alteration
Destruction
Enchant
Illusion
Mysticism

Mages Guild rank structure:

Rank	Intelligence	Willpower	One required Skill at	Two other required Skills at	Minimum Faction Reputation
1 - Associate	30	30	0	0	0
2 - Apprentice	30	30	10	0	5
3 - Journeyman	30	30	20	0	10
4 - Evoker	30	30	30	5	20
5 - Conjurer	30	30	40	10	30
6 - Magician	31	31	50	15	45
7 - Warlock	32	32	60	20	60
8 - Wizard	33	33	70	25	80
9 - Master Wizard	34	34	80	30	100
10 - Arch-Mage	35	35	90	35	125

Of course, these promotions don't come just based on your skills. You must perform quests to gain reputation and rank within the Mages Guild. You will typically receive 5 points of reputation for each successfully completed quest. Just ask about "duties" to anyone who has it in their conversation threads. Some of the Mages Guild quest givers do not want to talk to low-ranking members, so you should start with Ajira. The others can be done in no particular order:

Ajira, Guild of Mages, Balmora (will have two more quests once you reach rank 7)
Edwinna Elbert, Guild of Mages, Ald'ruhn (is very interested in the Dwemer, so you'll explore a lot of ruins for her)
Ranis Athrys, Guild of Mages, Balmora (persuade or kill off a lot of people who have offended her at one point or another)
Skink-in-Tree's-Shade, Wolverine Hall, Guild of Mages, Sadrith Mora (has an almost morbid fascination with vampires, so you'll be retrieving a lot of books and such on the subject)
Trebonius Artiorius, Guild of Mages, Foreign Quarter Plaza, Vivec (a real bonehead)

Typically, each rank requires two or three successfully completed quests in addition to the minimum stat and skills requirements.

You'll need to pay 200 gold in guild dues to be promoted to Rank 4 and you'll need to either purchase (5000 gold) or retrieve a Wizard's Staff in order to be promoted to Rank 8.

Each Mages Guildhall (except Caldera) has an Equipment Chest that you are welcome to use. The chest usually contains a couple of useless books, some Lesser Soul Gems, three somewhat useful scrolls and a couple of potions. You can take whatever you want from the chests, but it will take a few months (four, if the help file in the Construction Set can be believed) before it will restock.

Trebonius only has two quests:

Find out what happened to the Dwarves: you'll find the information that you need by completing all of Edwinna Elbert's quests. It's more or less just kind of laying around in the places she sends you. Specifically, you need three books: Hanging Gardens, The Egg of Time and Divind Metaphysics. Take those three books to either Yagram Bagarn in the Corprusarium at Tel Fyr or to Baladas Demnevanni at Als-Drelen in Gnisis and follow the conversation threads. Then report back to Trebonius. Your reward is a 20-point faction rep boost (which should be enough for a couple of promotions) and the clear indication that the Arch-Mage is completely clueless.
Kill all of the Telvanni council members: you can't get this until you have completed the Main Quest and have finished his first assignment. By that point in time, you've most likely already killed Trebonius in order to become Arch-Mage, but if you can restrain yourself, this one should be available to you. Your reward is another 20-point faction rep boost, the Necromancer's Amulet and Trebonius' Staff. Since you would pick up the staff and amulet after killing Trebonius, anyway, the question is whether the whole mess is worth 20 points.

Oh, and if you're ever expelled from the Mages Guild, you're told to go talk to Trebonius to make amends. The only problem is that he never seems to get around to it. The moral of the story? Don't do anything to get yourself expelled.