Edwinna Elbert Ald'ruhn Mage's Guild Quests
Edwinna Elbert is the NPC who offers you Mage's Guild quests in Ald'ruhn. The first 5 quests from her require no rank in the Mage's Guild, however, once you reach the Dwemer Tube from Arkngthunch-Sturdumz quest you'll need to be at least the rank of Conjurer to continue with her quests.
Edwinna Elbert Quest #1 - Chronicles of Nchuleft
For your first task from Edwinna Elbert you'll be asked with retrieving the Chronicles of Nchuleft book from one of many different places. The easiest location (imo) to get the book is the Balmora Bookseller. Below are a couple more easy locations to find.
Where to buy Chronicles of Nchuleft:
1. Dorisa Darvel, Balmora Bookseller
2. Jobasha's Rare Books in Vivec, Foreign Quarter
3. Vasesius Viciulus, Trader in Molag Mar
4. For a list of all locations check the Chronicles of Nchuleft UESP Entry
Edwinna Elbert Quest #2 - A Potion from Skink-in-Tree's-Shade
Speak with the Mage Guild Guide for quick travel to Sadrith Mora - then speak with Skink-in-Tree's-Shade who is found in the same room as the teleporter. Talk to him about the Detect Creatures Potion and he'll immediately give it to you along with tell you to return to him when you want some quests.
Note: You have to speak with Skink-in-Tree's-Shade for this quest. Even if you have a Detect Creatures Potion you'll have to head over to Sadrith Mora and speak with him anyway.
Edwinna Elbert Quest #3 - Steal Chimarvamidium
This is another insanely easy task. Take the Guild Guide to Vivec and find Sirilonwe's room - she's in the Mage Guild so it shouldn't be too hard to find her. Inside her room you'll find a small closet with "Sirilonwe's Chest" inside; close the door and use one of the Ondusi's Unhinging Scrolls that Edwinna gave you. Or whatever spell/method you have for opening the chest.
Edwinna Elbert Quest #4 - Huleen's Hut
Our next destination is Maar Gan; take the Silt Strider from Ald-ruhn to Maar Gan. You can find Huleen's Hut just outside of Maar Gan along the southeastern path, use my map for better directions. Inside Huleen's Hut you'll find a Scamp that you need to defeat. After it's dead speak with Listien Bierles, Huleen's Apprentice, to complete this part of the quest.
Edwinna Elbert Quest #5 - Return Chimarvamidium
Return Chimarvamidium to Sirilonwe in the Vivec Mage's Guild. You can either directly hand her the book (you'll get bonus Disposition with her if you do) or place it back inside the chest that you stole it from. Either way, when you're done return to Edwinna and tell her.
Edwinna Elbert Quest #6 - Dwemer Tube from Arkngthunch-Sturdumz
All you need to do for this quest is to collect a Dwemer Tube from any of the Dwemer dungeons throughout the entire game. There is a long list on UESP for this quest if you'd prefer to get the Dwemer Tube elsewhere rather than venture to Arkngthunch-Sturdumz. If you already have a Dwemer Tube in your inventory when you speak with Edwinna Elbert you'll be able to give her that one.
The Dwemer Tube in Arkngthunch-Sturdumz is found in the southeastern most room sitting on a shelf (pictured above).
Edwinna Elbert Quest #7 - Nchuleftingth Expedition
When you arrive at Nchuleftingth you'll meet Senilias Cadiusus and his daughter, speak with them for a Journal entry. For the next part of this quest you'll have to explore the Dwemer Ruins until you find the Test of Pattern section, use the eastern-most crank here to reveal a door to the Lower Levels.
Loot the corpse of Anes in the Lower Levels for the Senilis Report, while you're down here you'll want to also grab the Hanging Gardens of Wasten Coridale book which is right next to his body. Return to Senilias Cadiusus and tell him what happened to Anes then return to Edwinna Elbert in Ald'ruhn to complete the quest.
Edwinna Elbert Quest #8 - Scarab Plans in Mzuleft
For our penultimate quest from Edwinna we're going to be heading over to Dagon Fel. You can reach this location via boat, from Ald-ruhn take the Mage Guild Guide to Sadrith Mora then take the boat to Dagon Fel. Once here you'll want to travel a little bit southwest to Mzuleft; if you have Levitate it'll help you easily get over the mountain in the way.
Inside Mzuleft the Scarab Dwemer Plans that we need are in the first room to the right of the entrance. Next to the Scarab Dwemer Plans you'll also find the Mzuleft Key which will open many of the doors in this dungeon allowing you to explore the rest of it. Either way, when you're done return to Edwinna.
Edwinna Elbert Quest #9 - Bethamez
The final quest from Edwinna has us travel to Gnisis where we'll venturing down the eggmine and to the Dwemer ruins. You'll find the entrance of the eggmine on the eastern end of town but it's locked - you'll be able to buy a pass from Abelmawia (sometimes) or bribe the guard outfront of the mine for the key instead.
Alternatively you can take the underwater entrance a little further east in the water, which is also shown in my screenshot above. You can find the entrance to Bethamez inside of the Lower Eggmine portion of the Gnisis Mine. Not too far into Bethamez you'll find a table with the Dwemer Airship Plans ontop (pictured below). Once you've grabbed these you're free to leave and return to Edwinna to turn in your quest.