Morrowind:Mystery of the Dwarves

Quick Walkthrough
#Talk to Trebonius Artorius at the Guild of Mages in Vivec for duties.
#Collect the three books: Hanging Gardens of Wasten Coridale, The Egg of Time, and Divine Metaphysics.
#Speak to Edwinna Elbert in Ald'ruhn.
#Speak to Hasphat Antabolis in Balmora.
#Speak to Baladas Demnevanni in Gnisis.
#(optional) Speak to Divayth Fyr in Tel Fyr.
#(optional) Speak to Yagrum Bagarn in the Corprusarium.
#Return to Trebonius Artorius with the information.

Detailed Walkthrough
Duties
Trebonius Artorius in the Vivec Guild of Mages will first ask you to investigate the disappearance of the Dwemer (also known as Dwarves). He doesn't seem to have a good idea on how to do this, and he doesn't even seem to care very much about how you do this, though he suggests to speak with Edwinna Elbert at the Ald'ruhn guildhall.

Gathering the Books
In the last few Mages Guild quests given by Edwinna you may (and should have) picked up three different books related to the Dwemer: Hanging Gardens of Wasten Coridale, The Egg of Time, and Divine Metaphysics. You may have also already talked with Hasphat Antabolis at the bottom of the Balmora Fighters Guild or Senilias Cadiusus in Nchuleftingth who mention that Hanging Gardens of Wasten Coridale may be a key to deciphering the other two books. Since this book is written in Aldmeris, you will need to find someone who can translate it.

Finding a Translator
Since you've done so many Dwemer-related quests for Edwinna, she's the logical starting point for anything further Dwemer-related. After discussing "The Egg of Time" with her, she will point you to a fellow scholar, Hasphat Antabolis, though neither one of them can fully understand the three texts. It seems Aldmeris is over their heads. They don't mention anyone by name but Baladas Demnevanni in Gnisis' Arvs-Drelen is the next stop. If you have joined House Telvanni you may have already encountered him, and will probably be aware that he's also something of a Dwemer historian, and fortunately he's more familiar with Aldmeris. Baladas will give you enough information to report back to Trebonius to finish the quest, but if you want a more complete story, you'll need to speak to someone even older. Possibly the oldest character in Morrowind is in Tel Fyr. Speak with Divayth Fyr and he'll mention that he has the last living Dwemer, by the name of Yagrum Bagarn, living in his Corprusarium. Yagrum, of course, can understand the books written in Aldmeris and will offer overviews of them along with his own theories.

Return to Trebonius
Although you don't get any definitive, conclusive answers, discussing the Egg of Time with either Yagrum or Baladas while you also have Divine Metaphysics, constitutes successful completion of the quest (for Baladas you must also have Hanging Gardens). Trebonius will be shocked that someone actually completed one of his missions, and he'll try to play it off like he's not in way over his head. His Disposition will increase, and you'll get +1 Reputation.

Notes
Becoming Arch-Mage by force before completing this quest blocks you from completing the final step because you'll have killed Trebonius. Complete this quest before slaying your way to the top of the Mage's Guild.
You can take a shortcut and speak to Yagrum Bagarn straight away once you have The Egg of Time and Divine Metaphysics.

Quest Stages