The quest is given by Arch-Mage Savos Aren, who will be in the Hall of the Elements, sitting on a bench, looking at the Eye of Magnus. Talk to him to obtain the quest. After completing the quest, speak to the Arch-Mage again, and he bestows the Mage's Circlet as a reward. He says, "This circlet once proved invaluble to me. I hope it can be of use to you now."