Personal Quest
If the player helps Onmund retrieve his family's amulet, he becomes a possible companion character and marriage option.
The option to speak to Onmund about assisting him will appear after completing Under Saarthal, once the Eye of Magnus is relocated to the College's Hall of the Elements. Onmund will direct you to Enthir, who will offer a Radiant Quest to the player; Enthir will agree to return the amulet to Onmund provided the player succeed in retrieving a staff located in a chest from a random dungeon. This dungeon will be marked on the player's map once s/he agrees to help Enthir.
Related ThreadsOnmund - Needs Help! - last post by @ Jan 1, 2012
Onmund's request glitch? *possible spoilers* - last post by @ Dec 30, 2012
Onmund's Request. Please help me. Ps3 - last post by @ May 7, 2012