How to trigger quest: First, you must be a MASTER of RESTORATION spells to even have a chance of starting this quest. Once you have attained level 90+ in Restoration (I KNOW it is level 90+, as I was at 90) go find Colette Marence in the College of Winterhold. Ask her “what else” can be learned about Restoration and follow the dialog to get this quest to pop.
Colette will be pleased that you’ve taken such an interest in Restoration, and will remark that it is time for you to go see the Augur. It turns out, as she explains, that the Augur (who I’m sure you’ve met during the College of Winterhold questline) is an EXCEPTIONAL Restoration magician. However, he is very selective on who knows the MASTER Restoration spells…
Head down to the Midden and then the Midden Dark and talk to the Augur. He will tell you that to learn the spells you must be tested. Once you are ready you have to step into the light. Once you do, GHOSTS will start attacking you. Your goal here is to simply stay alive. A total of THREE ghosts will attack you down here, alternating between melee attacks and magic.
You, on the other hand, cannot hurt them and must survive using your healing magic. You will also be stripped of all your clothes and not allowed to use items (to be fair I never tried, but that’s what the Augur says).
Staying alive should be fairly easy for you if you’ve managed to make it THIS far (leveling restoration is no easy feat after all). You can run around and dodge the ghosts melee attacks of course, but the magic WILL make you eat some damage. After 3 minutes or so (I didn’t time it) the Augur will claim you have passed the test, and will reward you with the Master Restoration spell “ Bane of the Undead “. You will now be done with this quest.
Note that you can go back to Colette and she will have one more Master spell for you to buy and learn: “ Guardian Circle “. Be sure to check it out!