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Like the Fighters Guild, the mages have guilds in Vivec, Balmora, Ald'ruhn, and Sadrith Mora, plus an additional location is Caldera. Each location has a teleportation service that only members can use. You can be teleported to any of the other mage guilds in Vvardenfell. There are quest-givers in each guildhall with the exception of Caldera. Balmora's guildhall has two people you can see for quests. We'll get started in Balmora.
Favored abilities: intelligence and willpower
Favored skills: alchemy, alteration, destruction, enchant, illusion, mysticism
Friends: Imperial Cult, Hlaalu, Thieves' and Fighters Guild s, Imperial Legion
Foes: Sixth House, Telvanni; Temple; Redoran, Ashlanders, Camonna Tong, Vampire Clans
Special feature: ability to utilize teleportation service between mage guild locations
Conflict with a miscellaneous town quest: if you remove Trebonius Artorius from the game, you cannot get the quest from Tarer Braryn (in Vivec's Hall of Justice in the Office of the Watch) to speak to Trebonius on his behalf (makes sense, doesn't it?).
Ranis is just inside the Balmora Mages Guild. Talk to her to join the guild, but she doesn't have any quests for you just yet. Don't fret, downstairs you will find Ajira, who has some introductory quests for you. After you've done her quests, you can go see Ranis for some of hers. Later on, we'll check back with Ajira and she'll have two additional higher-level quests for you.
Ajira is the Khajiit downstairs in the Balmora guild behind the desk in the teleportation area.
Ajira will ask you to retrieve one each of the following mushrooms: violet coprinus, bungler's bane, hypha facia, and luminous russula. You can find all of these on the western side of the Odai Plateau, which is south of Balmora and east of Hla Oad.
Plant Fake Soul Gem
Next Ajira will ask you to place a fake soul gem in Galbedir's desk, which is just upstairs in the guild. No one should be around the desk, making your job easier -- just put the fake gem inside and report back.
Didja like getting the mushrooms? Well, now you can go pick flowers. Ajira wants one of each of the following: gold kanet, stoneflower petals, willow anther, and heather. You'll be directed to the shore of Lake Amaya to find them, but these flowers are not particularly rare and you can find them in various locations.
Get a Ceramic Bowl
Frisky little Ajira wants a ceramic bowl. Ra'virr sells them at his shop in Balmora, just to your left as you exit the guild. Return to Ajira with the bowl and you'll almost complete the quest…
Find Stolen Reports
Forget the bowl -- Ajira has had her mushroom and flower reports stolen (by Galbedir, no doubt) and you must find them! Leave Ajira and hang right. On your right in a partitioned area is a closet -- just under it you should see part of one of the reports. Grab it. Then head upstairs. At the foot of the stairs that lead to Galbedir's desk is an area with some baskets and such. Poke around there and you'll see the tip of the other report hidden amid the baskets. Bring these reports back to Ajira. And don't forget to give her the ceramic bowl from before. Ajira is done with you for now, but we'll check back with her later.
Once you're done with Ajira's introductory quests, you can go see Ranis for advancement within the guild. This advancement will entitle you to receive her quests.
Recruit Llarar and Collect Dues from Manwe
Ranis will toss you 2 quests concurrently to get you started. One task is to talk to Llarar Bereloth in Sulipund and get him to join the Mages Guild. The other task is to collect guild dues from Manwe in Punabi. Sulipund and Punabi are both north of Lake Amaya (which is in turn, north of Marandus). At the western tip of the lake there is a trail that bears north and slightly east. Taking this trail you will first encounter the cave Punabi. Head in and find Manwe just inside. You can boost her disposition up and she'll pay, you can kill her, or you can pay out of your own pocket when you return to Ranis. Leave Punabi and continue along the trail northeast until you reach the Velothi dome, Sulipund. Inside the dome on the top section, is Llarar. You can boost his disposition so he'll join or slay him. Psst! Special hint: grab the copy of the Chronicles of Nchuleft while you're here. Tell you why later. Head back to Ranis with the results of these two quests.
Pay Your Dues
If you're following me along step-by-step, Ranis will require that you pay your guild dues now, too. It's 200 gp. Cough it up, cheapskate. If you're winging it, you'll be asked to pay these dues sooner or later anyway, by whomever you're doing quests for at the time.
Stop Unsanctioned Training
Only-He-Stands-There is an Argonian in the basement of the South Wall Cornerclub who is offering restoration training. Ranis wants you to put a stop to it. You can kill him or make a deal with him on the side. If you're in the Thieves Guild, I'd suggest going with the deal option. Regardless, report back to Ranis.
Get Itermerel's Notes
Next Ranis wants you to escort Itermerel from the Eight Plates in Balmora to the Halfway Inn in Pelagiad. Well, not really. She just wants his notes. You can just kill the guy and loot his notes. If you escort him to Pelagiad and talk to him inside the Halfway Inn, he'll give you his notes. Keeping him alive gives you an interesting (?) option later on regarding Ranis' final quest, plus it's probably the nice thing to do.
Stop the Necromancer
Tashpi Ashibael in Maar Gan is practicing necromancy and she must be stopped. At least that's what Ranis says. In Maar Gan, you can talk to Tashpi first and it seems like she's not really practicing necromancy. This is another scenario wherein you can make a deal to let Tashpi split unharmed or you can just kill her. If you keep her alive, and you let Itermerel live, it'll open up an option in Ranis' next, and last, quest.
Find the Telvanni Spy
You can waste a lot of time with this quest by doing your own investigative work if you want. Or, once assigned the quest, you can go to the Vivec Mages Guild and talk to Trebonius, the current Arch-Mage, about the Telvanni spy. It'll bring up the question of Tiram Gadar's legitimacy -- and you can ask to see his credentials. If you look at them, they are indeed fakes. Return to Ranis and turn the spy in. Here's the twist I mentioned before: if you let Tashpi and Itermerel live, you will get an option to turn Ranis in to Trebonius as the spy. This is your call. Personally, I think they are both spies, or at the very least, Tiram forged his resume to get his job. I usually let Ranis live, but it will not make a difference since this is Ranis' last quest anyway, and Tiram has no game value alive or dead.
Edwinna is in the Ald'ruhn Mages Guild, wandering around the main room downstairs.
Get Chronicles of Nchuleft
It's a book. Go get a copy and turn it over to Edwinna. Buy it at Jobasha's Rare Books in Vivec's Foreign Quarter Lower Waistworks. Or, find a copy in the following locations: the Holamayan Monastery, in Molag Mar at Vasesius Viciulus' trader shop, in the Dwarven ruin of Nchuleft (not surprisingly), back in Sulipund (did you take the copy when I said to?), in Tureynulal (Kagrenac's Library), and in Vivec's Hall of Justice Secret Library.
Retrieve Potion from Skink-in-Tree's-Shade
Use the teleport to visit Skink in the Sadrith Mora guild and get the detect creatures potion from him. Take it back to Edwinna.
Borrow Chimarvamidium from Sirilonwe
And by "borrow" I mean temporarily steal. Go to the Vivec guild and find Sirilonwe. In a small room adjoining her own is a chest. Step in the little room, close the door, and pick the chest. Take the book in question and bring it back to Edwinna.
Investigate Huleen's Hut
Go to Maar Gan. Just outside the city to the east is Huleen's Hut. Inside is a scamp. Kill it. Go downstairs and unlock the door with Listien Bierles inside. He'll explain what happened so that you can report back to Edwinna. Wasn't that fun?
Return Chimarvamidium to Sirilonwe
Can't state it any more simply than that. Okay, maybe I should at least clarify one thing -- you're returning the book to the chest you stole -- er, I mean, borrowed -- it from in the first place. You're not giving it to Sirilonwe. You do not want Sirilonwe to know you ever had it. Can you handle it?
Get a Dwemer Tube
Any one will do. Edwinna will suggest exploring the Dwemer ruin, Arkngthunch-Sturdumz, but there are Dwemer tubes in most of the Dwemer ruins in the game. Take your pick and then bring your tube to Edwinna.
Acquire a Wizard's Staff
If you're following along with me, Edwinna will tell you that you need a Wizard's Staff (what wizard would be complete without one?). You can buy it off her right there (5,000 gp), or find one at either of the two following locations I'm aware of: the Daedric shrine of Ramimilk, or the Urshilaku Laterus Burial. Once you get it or buy it, she'll allow you to begin your next quest.
Get Excavation Report in Nchuleftingth
Your first of three Dwemer ruin quests. Nchuleftinght is at the point in the middle of being east of the cave Mababi, west of the Arethan Ancestral Tomb, and north of Mount Kand. Go there and once inside, hang a right to find and talk to Senilias Cadiusus. He'll send you off to find Anes Vendu who has the excavation report. Head to the section called the Test of Pattern, and activate the third and last crank on the left wall to open a secret door on the right wall across from it. This'll take you toward the Lower Level where you'll find Anes' dead body and the excavation report. Grab the copy of Hanging Gardens on the ground near the body, too. Report back to Senilias and then bring the report back to Edwinna.
Find Blueprints in Mzuleft
South of Dagon Fel is your next ruin, Mzuleft. There's a lot of Orcs to kill inside, and you'll find a Dwemer scarab schematic and a book called The Egg of Time. Grab the schematic and the book and head back to Edwinna.
Find Blueprints in Bethamez
Bethamez is a ruin inside the Gnisis Egg Mine. So head to Gnisis, and enter the egg mine. Oh, by the way, you can't just stroll in. It's locked and there's an Imperial Legionnaire guarding the entrance. You can pick his pocket, kill him, use stealth to pick the lock in his presence, talk to him about the egg mine (assuming his disposition is adequate), or have a miner pick in your inventory to get the key. Just get in. Inside, head toward the Lower Egg Mine and then to Bethamez. The Dwemer ruin of Bethamez is small and the plans will be easy to find. And hey, grab the copy of Divine Metaphysics while you're there. Hang on to these three books you acquired. Report back and you're done with the quest and Edwinna.
Ajira in the Balmora Mages Guild will have two advanced quests for you to do, so let's pay her a visit.
Find the Staff of the Magnus
Once you are a Warlock in the guild, you can talk to Ajira and she will direct you to Assu, a cave on Mount Kand (straight north from Molag Mar). Inside the cave, among other baddies, is Dreveni Hlaren, the current owner of the staff. Kill, collect, and head back to Ajira with the tale of your success.
Find the Ring of the Warlock
Ajira will also tell you where you can find this ring. Vindamea Drethan has it, and she lives in Ashirbadon, a cave on an island east of Bal Fell. Once you've acquired the ring, you can go and tell Ajira. She has no more quests.
Skink is in the Sadrith Mora Mages Guild, which is located in Wolverine Hall.
Don't panic, it's as brief as an escort job can be. Tenyeminwe is in Dirty Muriel's Cornerclub, and you only have to get her to the Sadrith Mora docks. Do that and report back.
Get Vampires of Vvardenfell Volume II
Not too common a book. Copies can be found in the following locations: the Galom Daeus Observatory, Mawia, Odirniran (in the tower), the Tel Vos Central Tower, Vas (in the tower), the Vivec Hall of Justice Secret Library (multiple copies!), and in Tureynulal (Kagrenac's Library). Bring one back to Skinky. If you go with Galom Daeus, Tureynulal, or the Secret Library, help yourself to a copy of Galur Rithari's Papers while you're there.
Arrange a Meeting
With the Ahemmusa. Go to the Ahemmusa Camp and speak with the wise woman, Sinnammu Mirpal, in her yurt. She will send you off to the Favel Ancestral Tomb to talk to her apprentice, Minabibi. Go to the Favel tomb and talk to Minabibi, and she'll tell you that the spirit of Kanit Ashurnisammis has to be killed. Go farther into the tomb and kill the spirit. Report back to Minabibi and then report back to Sinnammu (who'll ask you who killed the spirit -- I always say it was me, but I don't think if it matters if you lie) and then report back to Skink.
Kill Telura Ulver
Go to Shal and kill her. Shal is a cave north and west of Hla Oad, and directly north of the Daedric shrine, Ashurnibibi. It's to the west of the lake that is north of Hla Oad.
Soul Trap an Ash Ghoul
Skink will give you a grand soul gem and some scrolls to trap a soul and then ask you to trap the soul of an ash ghoul. Okay. The suggested location is Yakin, a cave serving as a Sixth House Base on the mainland shore northwest of Tel Aruhn. What are you waiting for?
Get Galur Rithari's Papers
There's a copy in Galom Daeus, Tureynulal, and the Vivec Secret Library, but you already know that because I already told you so, and you already got a copy because it made sense to do so. Surprise Skink and give him the book on the spot.
Technically, that's it for the Skinkster, but he'll give you a unique amulet and a letter you can present to Trebonius. Your next quest-giver will be the Arch-Mage, but the letter Skink gives you will give you an option to assume the title of Arch-Mage by presenting it to Trebonius. But let's start talking more about Trebonius.
The Arch-Mage is in the Vivec Mages Guild at the foot of the stairs. You have a few options here. You can ask him to be Arch-Mage and challenge him to a duel in the Arena. He'll accept, you have to go there, and then you fight him -- if you win, you're the Arch-Mage and you get to loot his amulet and staff. You can also do 1 or 2 quests for him. One involves the 3 books you got: Hanging Gardens, The Egg of Time, and Divine Metaphysics. The other is only available if you completed the main quest already: he'll ask you to kill all the Telvanni Councilors. After doing his quests you can also challenge him for the title. Or you can present him with Skink's document at any time and he'll retire and you'll assume control of the guild.
Investigate the Disappearance of the Dwarves
You can investigate all you want, but to bring the quest to a swift resolution, take the 3 books from Edwinna's last three quests to Tel Fyr. Travel all the way down in the Tower of Tel Fyr to the Corprusarium Bowels and locate Yagrum Bagarn. Explore all the conversation topics he presents to you and you can go back to Trebonius. If you didn't complete the main quest, this was his last quest, and you need to decide how you want to become the grandmaster. If you did complete the main quest, Trebonius will offer one more task:
Kill the Telvanni Councilors
These characters are involved in some minor quests, and the Telvanni quests. But otherwise, with the main quest done, it is okay to kill them (no game-breakers). Their names and locations: Master Aryon is in Tel Vos, in Aryon's Chambers, whose door is inaccessible without levitation. Mistress Dratha is in the Upper Tower of Tel Mora. Mistress Therana is in the Upper Tower of Tel Branora. Master Neloth is in the Tel Naga Tower in Sadrith Mora. Master Baladas is in Arvs-Drelen in Gnisis. Master Gothren is in the Upper Tower of Tel Aruhn. Kill ‘em all, and Trebonius will give you his staff and amulet.
Regardless of how you handled it, you're the Arch-Mage now. Cheers!