mage gild

What you need to do is go to the Cheydinhal Mages Guild, (Make sure your you have over 200 maximum encumberance points though, you`ll know why in a minute)speak to Falcar and ask to join. Once you have joined you will need to earn recommendations from each of the mages guild leaders before you can get into the Arcane University in the Imperial city. Now, just to get you on your way I`ll tell you about the first one. Falcar will ask you to retrieve for him a ring of burden which is located in a locked well behind the Mages Guild. He`ll tell you to speak to Deetsan (an Argonian)to get the key. Before you do though, wait until he is out of earshot (doesn`t matter if he is in the same room as long as he is in an opposite direction far enough from Deetsan). Once you have the key you can now access the well. You`ll soon see why you need over 200 maximum encumberance points because the ring burdens you by 150!
I hope I`ve been helpful.

Speak to the leader of any mages guils and ask about joining the mages guild.

Hope this helps!

You need to enter the mages guild by speakin' with any one the leaders of the citys bar the Imperial city