Rejoining the College

Not a good quest to have to complete. It is probably better to load an earlier game.

Walkthrough
You get this quest after killing someone related to the College of Winterhold such as a students or one of the instructors.

Speak with Tolfdir
You then have to speak with Tolfdir,...

Give Tolfdir 250 / 500 / 1000 gold to lift your suspension
... and pay him a fine between 250 and 1000, depending on your transgression before you are forgiven.

Neubeginn in der Akademie