You have to fight your way past Cliff Racers and leveled Red Mountain creatures to get to the entrance. Again, I find it much easier to simply levitate to avoid the drain on resources.

Tureynulal is built in four sections and you'll enter into Kagrenac's Library from the outside. Aside from wanting to take care of the seven ash vampires, there are four reasons to come here. First, you will need a copy of Kagrenac's Planbook for Yagrum Bagarn if you need to activate Wraithguard. Second, Skink-in-trees-shade will want a copy of Galur Rithari's Papers and one of the four copies available in the game is here. There is also a copy of "Vampires of Vvardenfell, Volume 2," if you don't feel like buying it from a bookseller. Third, you are a vampire in need of a cure and, again, you need a copy of Galur Rithari's Papers to do it. Fourth, Uvoo Llaren will send you here to retrieve the Cleaver of St. Felms as a Temple quest.

Kagrenac's Library:

There is not much in the Library section. A leveled Ash Creature will be directly in front of you when you enter (a good reason to "Sneak" before entering). The door to your right (north) leads to the entrance to the Eye of Duggan. The door to your left (south) leads to the Eye of Thom Wye. Behind the doors in front of you and down the stairs is Dagoth Molos (an Ascended Sleeper). The passageways on either side of Dagoth Molos both lead to the Bladder of Clovis. The whole place sounds like an anatomy lesson, doesn't it.

In the room behind Dagoth Molos is Dagoth Turyenul and another leveled Ash Creature. Kagrenac's Planbook is in the desk against the back wall.

Dagoth Tureynul is apparently quite the reader because you'll find a copy of almost every non-skill-raising book in his little library, plus five skill-raising volumes:

The rest of the passageways end at the entrances to the other sections.

Dagoth Tureynul (30th level Ash Vampire): 300 HP/500 MP, no weapons no armor

Eye of Duggan

A round tower room containing Dagoth Fals (an Ash Ghoul), a bunch of containers (ingredients, mostly), a few ingredients, and "36 Lessons of Vivec, Sermon 10" (Short Blade).

Eye of Thom Wye

Another round tower room containing Dagoth Galmis (an Ash Ghoul) and some more containers (the closet has some Dwarven Armor and a Dwarven Warhammer).

Bladder of Clovis

A rectangular room containing Dagoth Fandril (an Ascended Sleeper), a few barrels and the body of Mendel Eves (where you'll find the Cleaver of St. Felms and a few other goodies). Oh, and if you're in need of it, there are 10 gold pieces laying around here, too.