I'll be perfectly frank at the outset. I do not like this lady in the least. Do you notice a theme to all of her quests? It's "my way or the highway" as far as she's concerned and the "highway" is a one-way ticket to the cemetery. This lady is absolutely ruthless in protecting the prerogatives of the Mages Guild and is not above using you to settle a couple of old scores along the way. Methinks her best interests would have been served by House Telvanni, but perhaps she was too bloodthirsty for them and had to settle for the Mages Guild.
Be that as it may, she has the only other Mages Guild quests in Balmora. Once you have reached the rank of Journeyman, she will have some duties for you. If you have completed Ajira's quests, this should not be a problem. In addition to quests, Ranis will also sell spells and train you in Mysticism (54%), Alteration (48%) and Illusion (48%) once you reach the proper rank (should be either rank 3 or 4).
You may take this quest and the next one at the same time. In fact, Ranis encourages you to take care of both at the same time. You do not have to, but since the locations you need to visit are very close to each other, there really is no reason not to.
There is a former Telvanni sorcerer named Llarar Bereloth living in a house named "Sulipund". The way that you get there is fairly simple. Head toward Fort Moonmoth and take the left fork where the road branches just before you get to the Fort. Then take the right fork where it branches next and follow the road (it's a long haul with lots of critters to keep you company) to Molag Mar. When you get to the lake, you'll go left and you'll find Sulipund just up the road from Punabi (the destination of the next quest).
Llarar Bereloth is a 7th level Sorcer who is NOT a former Telvanni (at least his faction affiliation is still showing as Telvanni). As a Telvanni, he doesn't like you very much just on general principles and dislikes you a lot because you are a member of the Mages Guild. This is going to make you job doubly difficult. His starting disposition should be somewhere near 20, so you've for your work cut out for you if you want to avoid the violent solution.
If you can get his disposition up to at least 70 (bribery generally works very well, but raising your Personality and applying a little flattery will also do the job), he will be putty in your hands and will swap sides.
If you cannot get his disposition up that far, you'll have to kill him. Since he's in the room by himself, you can do the dirty deed with little fear of interference from his friends downstairs (who are also Telvanni and who also dislike you for pretty much the same reasons). He has a short-bladed weapon that is tied to your level (but only a 31% skill with it), a 54% skill in Destruction and a good selection of spells to go with it. On the other hand, he's not a warrior-type, so his 75 health points should be fairly easy to knock down quickly.
After convincing Bereloth to join (or disposing of his lifeless corpse, whichever way your preferences go), report back to Ranis for a 10-point boost to her disposition, a 5-point boost to your rep with the Mages Guild and a Quality Potion of Restore Magicka.
A Mages Guild member is behind on her dues to the tune of 2000 golds. Ranis tells you to collect the back dues (in which case she will split it with you) or kill Manwe as an example to other deadbeat wizards. Manwe is in Punabi, a cave complex on the right of the road before you get to Sulipund.
Manwe, an 11th level Sorcerer (with no faction affiliation, so no one is going to be terribly honked if you have to kill her), is the first person you encounter. She'll be down at the bottom of the slope just inside the door. If you can get her disposition up to 60 or more, she'll fork over the cash if you will promise to leave her alone. If you cannot get her disposition up to 60 or more, you'll have to do it the hard way (she does have 200 gold on her, so the trip isn't a total waste, but I have no idea where she comes up with the 2000 golds for her dues). If you do have to take her out, avoid fire-base spells as she is 75% resistant to them.
If pillaging and mayhem are your thing, you will find three others in the cave:
Plus an assortment of the usual goodies that you'll find in almost any evil wizard's cave (potions, scrolls, books, money, etc.).
After collecting the cash or making a "dead"-beat out of the deadbeat, report back to Ranis for your reward. If you collected the money, you'll get 1000 golds, a 15-point boost to Ranis' disposition toward you, and a 5-point boost to your rep with the Mages Guild. If you had to kill Manwe, you won't get anything except a 5-point boost to Ranis' disposition and a 5-point boost to your guild rep.
An Argonian in the South Wall cornerclub is offering unsanctioned training in the magical arts. Since this is clearly the prerogative of the Mages Guild, you are to make him cease and desist. Ranis doesn't care whether he stops voluntarily or not, as long as it stops.
Since there is only one Argonian in the South Wall (Only-He-Stands-There), it should be fairly obvious who the unsanctioned trainer is. If you can get his disposition up to 60, he will agree to stop the unsanctioned training.
If his disposition is more than 40, but less than 60 (which it should be, unless you have managed to insult him prior to this point), he will offer you a deal, instead. If you will tell Ranis that he has agreed to stop the unsanctioned training, he will train you (and sell spells, too). Since he is one of the few people in Balmora who will train in Restoration, this is probably the way you should go. If you agree to this, report back to Ranis first and then he will train you in Mysticism (58%), Alteration (53%) and Restoration (53%).
Report back to Ranis for your reward. If you had to kill the Argonian, you'll get a 15-point boost to Ranis' disposition, a 5-point boost to your Mages Guild rep and 4 scrolls of "Elemental Burst: Fire." If you took him up on his offer and lied to Ranis about it, you'll get a 15-point boost to her disposition and a 5-point boost to your Mages Guild rep.
On the surface, this seems like a simple escort mission. It's the undertones that are disturbing. Itermerel, a scholar, has arrived in Balmora and wants to go to the Halfway Inn in Pelagiad. Ranis is happy to oblige (with you as the escort) as long as she gets a copy of his notes. You'll find Itermerel on the ground floor of the Eight Plates, just up the street from the Mages Guild. He should be right in front of you as you enter. If you try to talk with Ranis about Itermerel before you have his notes, Ranis' disposition toward you will drop by 5 points each time.
Just escort him to the Halfway Inn in Pelagiad. He will not give you the notes before you get there, but you can take them off of his corpse if that's the way you want to go. As with any escort mission, he will try to join any combat that you initiate. He's a 14th level Mage with a decent skill in Destruction, but only two Touch-ranged damage spells. He's got 84 Health Points, so as long as you don't start messing with Daedra, you should be able to get him there in one piece.
Once you reach the inn, let him catch up with you before you try to enter. Otherwise he'll just wander around outside and get lost. When you are inside the inn, open a dialogue and ask for his notes. He'll give you a copy and send you on your way.
When you have the notes (if you killed Itermerel to get them, Ranis will take care of your Guild expulsion for you), you'll get another 15-point boost to her disposition and a 5-point boost to your Mages Guild rep.
Your next assignment is to locate a necromancer named Tashpi Ashibael in Maar Gan and kill her. Don't argue, just do it. There's only one problem. There is no necromancer in Maar Gan. There is, however, a Healer named Tashpi Ashibael who refused Ranis' offer to join the Mages Guild several years ago. Hmmmm. Someone is carrying a big grudge.
Take the silt strider from Balmora to Ald'ruhn and then from Ald'ruhn to Maar Gan (it's a very long walk otherwise). Start asking around town about Tashpi and you'll find out that she's the town Healer and you can get directions to her hut. Go there and talk to her.
If you tell her that Ranis was the one who said Tishpi was a necromancer, she will tell you that she refused Ranis' offer to join the Guild and is surprised that she has held a grudge this long. Tashpi will suggest that it might be better for her to relocate to the mainland and have you tell Ranis that she is dead. If you agree to this, that's the end of the matter.
If you do not agree to the deception, you'll have to fight Tashpi (she's only a 5th level Healer, but she'll summon an Ancestral Ghost that doesn't disappear in a few seconds). Beware if you take this option, though. Your rep in Maar Gan will drop like a rock with everyone to whom you mention it.
Report back to Ranis. If you killed Tashpi, you will get a 20-point boost to Ranis' disposition, a 5-point boost to your Mages Guild rep, a 1-point boost to your overall Reputation, 2 scrolls of "Elemental Burst: Fire," and 2 scrolls of "Fourth Barrier". If you let her go, you'll get a 15-point boost to Ranis' disposition and a 10-point boost to your Mages Guild rep and the rest of the goodies.
Ranis believes that the Guild has been infiltrated by a Telvanni spy. Believe it or not, she's right. She wants you to investigate the Ald'ruhn, Vivec and Sadrith Mora Guildhalls and report back to her. For once she does not want you to take any action. Just find the spy and report back to her.
No one at any of the Guildhalls knows anything about a spy. The only mention you'll get is from Trebonius in the Vivec Guildhall who will point out Tiram Gadar as his Dunmer advisor who keeps an eye on that sort of thing for him. Talk to Trebonius about other matters and you'll quickly notice that Trebonius is an idiot. He must have had some seriously high connections in order to have snagged an appointment as Archmage of the Vvardenfell province because he certainly didn't do it on intellectual merit.
Be that as it may, Trebonius will give you a copy of Tiram Gadar's credentials if you ask about them. Read them to find that they are a forgery (the Archmagister's name is misspelled).
Talking to Tiram Gadar will net you a flat denial and a referral to Trebonius. If you follow up with Trebonius and name Gadar as the spy, Trebonius will not believe you and his disposition toward you will drop by 5 points. Which means turning the credentials over to Ranis (as you were supposed to do in the first place).
If you turn over Tiram Gadar's credentials to Ranis, you will get a 15-point boost to her disposition (which should be pushing 100 by now anyway), a 5-point boost to your Mages Guild rep, a 1-point boost to your overall rep, 2 scrolls of "Summon Golden Saint" and a Daedric Dagger with "Soul Trap" on it (perhaps you should use the scrolls to summon the Golden Saint so that you can then Soul Trap them? Sounds like a plan to me).
If you name Ranis as the spy to Trebonius, he will say that he can't believe it, but will expel her from the Guild immediately (she disappears from the Balmora Guildhall). You'll get a 5-point boost to your rep with the Mages Guild and a 1-point boost to your overall reputation.
My solution was to simply take care of two birds with one trip. I named Ranis as the spy (the lady was obviously unhinged) and then taunted Gadar into a fight to resolve the little spy problem. Trebonius wasn't too terribly happy with my solution, but my rep did not suffer with anyone.