The Argent Dawn Quests

Quests significant to gaining Argent Dawn reputation include:

Cauldron Quests 

While having a Vitreous Focuser in your backpack, certain items drop from undead monsters in Western Plaguelands and Stratholme; those items can be combined with Arcane Quickener and Runecloth to poison a scourge cauldron, gaining Argent Dawn reputation. Vitreous Focuser and Arcane Quickener can be acquired from an NPC in your faction's Western Plaguelands camp. The mobs at the first three cauldrons drop Minion's Scourgestones while some mobs at the fourth Cauldron drop Invader's Scourgestones. Therefore Gahrron's Withering is the best place to grind, if you can handle the level 56-58 mobs there.

After completing the first of the Cauldron quests, you can obtain a Vitreous Focuser from the Apothecary. There isn't any particular warning that you can obtain one, so pay attention and talk to your NPCs.

In order to complete the quest for cleansing a given cauldron 4 runecloth pieces are needed plus the following:

 [53] Felstone Field Cauldron (requires 6 Osseous Agitator from skeletal undead)

 [55] Dalson's Tears Cauldron (requires 5 Somatic Intensifier from zombie undead)

 [55] Writhing Haunt Cauldron (requires 5 Somatic Intensifier from zombie undead)

 [58] Gahrron's Withering Cauldron (requires 4 Ectoplasmic Resonator from wraithform or ghostly undead)

Dawn's Gambit 

The quest chain starts at Tinkee Steamboil in Burning Steppes with the quest Broodling Essence. In the end, you are able to get the item Dawn's Gambit from Betina Bigglezink at Light's Hope Chapel. Dawn's Gambit turns the students in the Viewing Room in Scholomance into easily killable skeletons, enabling you to kill Vectus and his assistant for another two Corruptor's Scourgestones and some reputation. Once the quest line is completed, you can request more Dawn's Gambits from Betina Bigglezink. (See the main Scholomance article for a complete set of links for the Dawn's Gambit chain.)

Healthy Scales 

After completing  [60] Plagued Hatchlings, players can loot a Healthy Dragon Scale from Plagued Hatchlings in Scholomance. The scale is not unique, and the quest it gives may be repeated for 75 reputation.

Other Quests 

Blackfathom Deeps

 [24D] In Search of Thaelrid - 1000 reputation

 [27D] Blackfathom Villainy (Alliance) - 1000 reputation

 [25D] Twilight Falls - 1000 reputation

 [27D] Blackfathom Villainy (Horde) - 1000 reputation

Desolace

 [33] Sceptre of Light - 500 reputation

 [38] Book of the Ancients - 700 reputation

Winterspring (ending in the Plaguelands)

 [52] The Everlook Report (Alliance) - 150 reputation

 [52] The Everlook Report (Horde) - 150 reputation

 [52] Duke Nicholas Zverenhoff - 150 reputation

Western Plaguelands

 [53] Scarlet Diversions - 100 reputation

Rewriting the Battle of Darrowshire quest chain - 1750 reputation

Eastern Plaguelands / Stratholme

 [55] Houses of the Holy - 1000 reputation

 [55] Zaeldarr the Outcast - 300 reputation

 [55] The Archivist - 1000 reputation

 [55] The Truth Comes Crashing Down - 1000 reputation

 [55] Above and Beyond - 1000 reputation

 [55] Lord Maxwell Tyrosus - 500 reputation

 [55] The Argent Hold - 1000 reputation

Temporary world event quests

 [60] Secrets of the Colossus - Zora - 800 reputation (Only doable within 10 hours from the Gates of Ahn'Qiraj world event)