If you specialize in magic, it is recommended to unlock the Winterhold Magic Academy early in the game. It is similar to the Magic Guild. You complete the tasks assigned by the mages, and they will teach you the knowledge of different types of magic. At the same time, you can also unlock some areas here.
1. The first lesson will be triggered when you come to Winterhold Magic Academy for the first time.
At the bridge leading to the academy from Winterhold, a magician named Faraudah will come to test your qualifications to enter the academy. You can cast any spell in front of him, or tell him that you are a dragonborn and show him the dragon's roar.
Faraudah is a magic teacher, you can learn destruction magic from her.
2. After entering the academy, go to the courtyard and report to Mirabelle Ewen. She will lead you to visit the academy. Along with this she also gives you a set of Cadet Outfits, be sure to equip them in your inventory.
3. Then follow Mirabelle into the Hall of Achievement. You will see many new students gathered here. You are assigned to a dormitory and then head to the Hall of Elements for classes.
4. You will see a teacher named Tovdir standing among the students and explaining endlessly, and then some students ask him to show some actual magic.
Tovdir will ask you what you think, and reply that he should learn something practical.
At this time, Tovdir will teach you the secondary enchantment technique. Enter the magic menu to equip it, and then use the secondary enchantment technique to defend against one of Tovdil's magic attacks to complete the task.