Is it permissible for someone who is in class to repeat the Adhan to himself before the muezzin finishes it, so that he can listen to the teacher?

Repeating the Adhan (call to prayer) is recommendable, not obligatory. It is permissible to repeat it before the muezzin if the muezzin is slow or if the listener is preoccupied, although repeating it after him is preferable. It is also permissible to suffice with repeating the Adhan up to the end of the Shahadatayn (the two testimonies of faith), and there is no harm in that.