Yesterday after 80+ hours play I finally got to the Mages college.

Urag the librarian asked me to get the Invocation of Azura, I already had it in my inventory, but it wouldn't offer it to him, so I went on the quest, and the book wasn't in the location indicated, and now I can't complete it.

Any ideas?

Have you tried dropping the book or placing it in a chest or bookshelf? Some quests won't update unless you do that. I had the same problem for that inn keeper that wanted those gems. I already had them but had to drop them and pick them up for it to reset.

got the same issue, cant drop the book due to it being marked an essential quest item.unless they patch it or you on pc guess we will both have it stuck in our journal unable to finish the quest.i went to every location i could go too.. spent time crafting etc.. just to have a dozen quests broken cause i chose to exlpore first

If you have a PC, type this in the console:

setstage MGR20 20

This will fix it, and won't break achievements!