Hannibal Traven gives you a task of leading a group of Battlemages preparing to storm some ruins to recover a special Black Soul Gem.
Head to the south of Cyrodiil, and arrive at Silorn. Meet the Battlemages there and speak to Thalfin. You are told to prepare the group to ambush the Necromancers when they leave the ruins. You can position the three Battlemages either up close, or at a distance. Each of the group have skills and will express where they may be best used. Thafin is best at close range, as is Iver, while Merete is best deployed further back.
The Necromancers will emerge and all hell will break loose. When Falcar retreats back into the ruins, your task is now to find and kill him. Head into the ruins, and make your way through the ruins. It's fairly large and mazy, and can be quite confusing. It's also full of Necromancers, so be careful.
Alternative Strategy: Before Falcar can make a run for it, you can get behind him and block his escape route and/or hit him with a paralyzing or burden spell/potion. It's a lot easier than trying to chase him through Silorn, but if you plan on looting the place and fighting all of the enemies in the dungeon anyway it doesn't really matter.
If you find yourself stuck, there is a hidden switch on a balcony up above that requires you to go through Silorn Sedorseli to get to. Once you find the switch, hit it and the gates on the bridge will open allowing you to get to Falcar (note: If your Agility/Acrobatics is high enough, you can actually leap up to one of the pillars and then up onto the balcony where the switch is cutting out the journey through Silorn Sedorseli). Falcar is pretty tough, but once he's defeated search his body and take the soul gem.
Head back to the University and give the gem to Traven to complete the quest.
Alternatively you could send them all further back and use invisibility to sneak up on Falcar and kill him without having to do all the painful dungeon delving.
If you can't get past the two gates that separate you and Falcar (the ones that are opened remotely) and you cant find the switch that opens them, you can always jump from the edge of the walkway and, using the left stick, land on the next piece of the walkway. You can do that with the second walkway also. (Not tested on PC version, confirmed on Xbox and PS3)
Also, where the two gates on the bridge are found around he outside you can jump on those, they are what make up the wall and easily jumped across,skipping all the wasted time.
After accepting the quest from Traven:
- I need to travel to the south of Cyrodiil and meet a group of Battlemages preparing to storm the ruins of Silorn.
After arriving at Silorn and speaking with Thalfin:
- I have arrived at Silorn, and spoken with Thalfin. We cannot enter the ruins, so I must help prepare an ambush for the Necromancers when they attempt to leave.
If you don't manage to kill Falcar outside, he flees:
- Falcar has fled back into the ruins of Silorn. I must find him.
After killing Falcar and retrieving the Black Soul Gem:
- I've recovered the Black Soul Gem. It needs to be taken back to Hannibal Traven at the Arcane University.
After delivering the gem to Traven:
- The Black Soul Gem has been delivered to Hannibal Traven.
If you accidentally kill one of the Battlemages during the initial fight and are suspended from the guild, Falcar won't fight you inside the ruins. He will only speak to you about your suspension, thereby forcing you to get back into the guild before finishing the quest.