The door is locked and I can't read the last book how do I get the key to the door?
According to UESP
The door prevents access to Neloth's staff enchanter and an arcane enchanter. It is possible to buy unenchanted staffs from Neloth and create your own staffs using the staff enchanter, but only if you prove useful to Neloth by completing a quest. This room also contains a Black Book titled The Hidden Twilight reading this will initiate the quest of the same name.
The quest that needs to be completed is The Reluctant Steward in order to unlock the door with the black book.