These are the main quests associated with the Museum. For the museum's side quests see Autres Quêtes.

Main Quest Name Description
Héritage brisé

Byron will start looking for you after you received the Sword of Ancient Tongues at 275 displays.

Once he sees you in the world space, he'll run up to you and hand over a shard and then die. Three Morag Tong assassins are chasing after him and attack you. This will activate the quest in the quest log. In order to speed up the process simply travel to any area outside of Whiterun and wait for Byron. The sword itself does not have to be carried and can be left on display in the museum.

The Ayleid Crossroads After finishing Shattered Legacy when returning to the Museum Auyren will come and talk to you.
Shadows of One's Past / Museum Heist

After Shattered Legacy is completed and you reached a display count of 400 this quest will start.

Une nuit au Musée / The Haunted Museum

The quest starts after 600 displays and after finishing the 'Museum Heist (Shadows of One's Past)'. When returning to the museum after fulfilling these prerequisites, Brother Ikard will speak to you before you can enter.

Les caveaux de Tréfonde The vaults of Deepholme is a quest that becomes available after discovering Deepholme.
Notes d'Auryen Description
Dague de Symmachus Une quête sans suivi pour retrouver la Dague de Symmachus.
Le sabre de Cyrus An untracked quest to retrieve Sabre de Cyrus.
Le Coffret du roi Orgnum An untracked quest to retrieve King Orgnum's Coffer.
Lame Glacée du Monarque An untracked quest to retrieve the Ice Blade of the Monarch.
Umbra An untracked quest to retrieve Umbra.
Le Heaume de Verdesang An untracked quest to retrieve the Heaume de Verdesang.
L'Anneau du Sorcier An untracked quest to retrieve the Warlock's Ring.
La Cuirasse du Dragon An untracked quest to retrieve the Dragonmail Cuirass.
Les Poings de Randagulf An untracked quest to retrieve the Fists of Randagulf.
Les Outils de Kagrénac An untracked quest to retrieve Sunder, Wraithguard and Keening.
Radiant Quests Description
Finder's Keepers A radiant quest that will send you to retrieve a new artifact for the museum.