Talk with him about what was found in Saarthal. He will tell the Dragonborn that a former student, Orthorn, stole the books as a peace offering to join a group of summoners. As you are leaving, you will encounter Ancano, a Thalmor Adviser. He will ask after what the Dragonborn was sent to report on. You can either confirm it or be evasive. Either way, head outside. It is time to go to Fellglow Keep.
Fellglow Keep is found to the East of Whiterun. Around the base of the crumbling keep, you will encounter a number of Mages who have summoned a Flame Atronach. deal with them and then head to the Southern part of this area. You will find a set of stairs leading down to the entrance to the Fellglow Keep Dungeons
Once inside the dungeon, head on down the slope. This leads to a watery room. Head over to the right-hand side of it and take the stairs up. There you will encounter an Apprentice Ice Mage and his two pets: Frostbite Spiders. Head on through to the South past him.
Be careful as you reach the bottom of the steps past this Ice Mage as there is a Trap trigger. Avoid it and continue down the stairs to the Northeast. There is an Apprentice Conjurer waiting at the bottom of them. This leads to the cells that the Mages here are keeping their "Test Subjects" (Vampires) in. Keep going along the corridor to reach the next big chamber.
Head to the middle of the room. There are 3 levers. To free Orthorn, just interact with the middle one. Interacting with the right-hand one will loose the inhabitants of that cell as well. Not too beneficial. Head over to Orthorn and talk with him. You can either tell him you came to rescue him (which will give you the chance to have him as a temporary follower) or just tell him you are there for the books. If you tell him that you are here for the books he will tell you what he knows then leave the area.
With that dealt with, continue forward through the area to the North. Follow the stairs down to find more Apprentice Mages (2 Ice and 1 Apprentice Fire Mage) to deal with. Once they are dealt with then head into the room they were in. Search the shelves to find some books. If you find the book Legend of Red Eagle it will trigger a miscellaneous quest to find his sword. After that go to the Northwest and follow the corridor there. This will lead to the next massive room. Inside here you will find a number of Skeletons and a small group of mages (Novice Necromancer). Defeat then and head on out of the area to the North. There you will find the entrance to the next area. This takes you to Fellglow Keep. Be sure to grab the spell tome(Raise Zombie) sitting at the end of the room to add into your inventory or skills.
Inside the keep go on up the stairs. There you will find more Mages: a Conjurer and a Storm Mage. Take out the Storm mage first as their spells will drain your own magicka. After the fight be sure to look on the podiums to find more Magical Tomes or the skill book The Doors of Oblivion. Head over to the East and go through the wooden door there. Another Necromancer awaits on the other side. Deal with him, head over to the left and then continue to the East. Head into the next room. Deal with the Flame Atronach and the 2 Mages. head over to the right and into the room with the Arcane Enchanter. Look on the table between it and the Alchemy Lab. You will find an Unusual Gem there, it is needed for another quest which is started when you collect this one. After that leave the room and head up the stairs opposite it to the East. Loot the Workroom that this staircase leads to. You are going to need a lot of what is found here.
Head South and to the West after you have looted the room. go on up the next set of stairs. You can look into the rooms in this corridor to find Mages. Kill and loot one of them to get the key for Fellglow Keep. Head through the door to the Northern end of the corridor. There is likely a Flame Atronach on the other side. Head up the stairs after that and approach the marked door. Interact with it to enter into the Fellglow Keep Ritual Chamber.
Once inside the Chamber, the Dragonborn will find The Caller. She is hardly happy with you coming into the Keep and killing her assistants and disrupting her work. You can talk with him to work somethings out but it should be expected to end badly. One alternative to fighting her is to trade her the books for Orthorn for the books.
If you take the route where you fight her, she will immediately summon one or two Atronachs. She will frequently teleport after taking a hit or two. The hard part is she will exchange her location with that of her summon. It will immediately attack you. She can be a tough fight. Be sure to have some Resist Shock to fight off her main attacks.
After the battle, loot her body for the Fellglow Ritual Chamber Key. Grab the marked books in the chamber and then go to the locked wooden door. Those books are Fragment: On Artaeum, Night of Tears and The Last King of the Ayleids. Head inside it and loot the remaining books found there. There are a number more to be found in the chamber plus some Soul Gems and other useful items. Head over to the trap door after you loot the room to quickly return to the front of Fellglow Keep. Just head straight to find your way back to Skyrim. From there just fast travel back to the College of Winterhold.
Track down Urag gro-Shub in the college and give him the books. He will tell you it's going to take some time to find the needed information. In the mean time he will give you a skill book for each school of magic: Withershins, Daughters of Niben, The Doors of Oblivion, Enchanter's Primer, Horrors of Castle Xyr, Racial Phylogeny and Incident at Necrom