Got the quest after I had already raided the dungeon and already got the book. But the quest giver at Mage's College does not acknowledge that I have the book and done the quest.
I cannot cancel the quest and start again because there does not seem to be a cancel quest option. Cannot throw the book away because it is a quest object. Cannot even store the damn thing.

Unfortunately a known bug. It can happen on any fetch quest. We'll have to wait for a patch, or if you're on the PC there might be some console workarounds.