I was wondering, is it possible for me write a book using the universe of Tamriel..?
because the magnificent universe that has been created in the elder scrolls, and all the history is so magnificent. and by just using it in the games would be a waste.

If i made a book about Tamriel, I would only use the history and the lands, not all the little details that you can find in the games.

I believe you are allowed to create fan fiction as long as you don't profit from it

Check out the Elder Scrolls Fanfiction area. You will have a new hobby for some time.