Go to the library.

You decide that you might learn some useful spells by going to the library. According to the map then there is two paths you can take to it.

One path would be a little long and it would take you through some weird crypts running under the school. Though from the map it appears that you might get acces to a restricted section.

The other path is quicker and runs through the dinning hall, that you just came from. Though it seems you will have to pass by the librarian to get into the library, this way.