So, I did all of the beginner quests for Ajira, but Ranis still tells me that I should look to Ajira for duties and she won't give me any of her quests. I did go to the Ald' ruhn Mage's Guild and did a quest there to find the Dwemer book but whenever I try to ask for an advancement it won't let me saying I don't meet the requirements. My guess is that it's stuck because it won't register that I did the quests with Ajira. Is there any way around this? Like to do something else to trigger it or perhaps something I could input in the console? Thanks.

When it says "requirements" it usually means that your skills (i.e. Mage guild "favored" skills) are not high enough. Restoration and Conjuration are NOT favored skills, the other 6 magic skills are.

You also need to have a sufficiently high level in the favored Attributes, Intelligence and Willpower. This is usually not a problem as anything over 35 is good for all ranks.

OMG!!! You're right!! Wow...I can't believe I didn't think about that at all. That probably is the reasoning. My character really isn't a mage. Was just doing the quests. I think Restoration is his only really high magic skill and it's only a minor skill at 18 or something? But yeah, that probably is the reason. Thanks a bunch, I'll go raise my skills and see what happens.

Yup, that was the thing that was missing. Just too low of skills. I went into the console and tinkered with that just to see and then they promoted me in ranks. Guess I just have some magic to be practicing. Thanks a bunch, jeabo.