The Algeth'ar Academy

If like me you were looking all over your map for where this might be then I've got some embarrassing news for you. Don't worry, it'll pass. Algeth'ar Academy is one of the dungeons in Thaldraszus, so this is just a poorly described dungeon quest.

this quest just requires you to run the Algeth'ar Academy dungeon. it'll be complete once you kill the final boss.

Where to pick up dungeon quests in Dragonflight 10.0.2

Gear rewards
The Algeth'ar Academy
Brackenhide Hollow: To the Source
Halls of Infusion: Entropy to Order
Neltharus: Secrets Within
Wanted: Earthbound Primordial Core
Ruby Life Pools: Primalist Invasion
The Azure Vaults
The Nokhud Offensive: The Wind Belongs to the Sky

/way #2112 61.6 36.2 Kalecgos (The Algeth'ar Academy)
/way #2024 13.2 49.4 Brena (Brackenhide Hollow: To the Source)
/way #2112 54.6 41.0 Watcher Koranos (Halls of Infusion: Entropy to Order)
/way #2022 25.0 56.2 Archivist Edress (Neltharus: Secrets Within)
/way #2022 46.7 82.9 Archivists' Request (Wanted: Earthbound Primordial Core (weekly))
/way #2022 59.8 76.0 Kildrumeh (Ruby Life Pools: Primalist Invasion)
/way #2024 39.4 63.0 Sindragosa (The Azure Vaults)
/way #2023 22.2 51.0 Khanam Matra Sarest (The Nokhud Offensive: The Wind Belongs to the Sky)

/run local a={72193,66211,72192,72135,71001,66119,71155,66339}for i,q in ipairs(a)do print(C_QuestLog.IsQuestFlaggedCompleted(q),C_QuestLog.GetTitleForQuestID(q))end

Low-ilvl gear rewards
The Nokhud Offensive: Founders Keepers
The Nokhud Offensive: The Final Ancestor

/way #2023 41.0 61.6 Ohn'ir Initiate (The Nokhud Offensive: Founders Keepers)
/way #2023 41.6 56.6 Elder Nazuun (The Nokhud Offensive: The Final Ancestor)

/run local a={66658,66690}for i,q in ipairs(a)do print(C_QuestLog.IsQuestFlaggedCompleted(q),C_QuestLog.GetTitleForQuestID(q))end

Reputation rewards
[quest=66874]
[quest=66860]

/way #2112 34.8 28.0 Kemora (Preserving the Past: Halls of Infusion)
/way #2112 34.8 27.6 Theldren (Relic Recovery: Legacy of Tyr)

/run local a={66874,66860}for i,q in ipairs(a)do print(C_QuestLog.IsQuestFlaggedCompleted(q),C_QuestLog.GetTitleForQuestID(q))end

All
/run local a={72193,66211,72192,72135,71001,66119,71155,66339,66658,66690,66874,66860}for i,q in ipairs(a)do print(C_QuestLog.IsQuestFlaggedCompleted(q),C_QuestLog.GetTitleForQuestID(q))end

Pre-requirements
Brackenhide Hollow: To the Source
[storyline=1316] questline starts with Breaching the Brackenhide at
/way #2024 15.2 39.4 Kalecgos (Breaching the Brackenhide)

The Nokhud Offensive: Founders Keepers
The Eternal Kurgans questline starts with Return to Mender at
/way #2023 39.0 66.0 Initiate Zorig (Return to Mender)

The Nokhud Offensive: The Final Ancestor
Elder Nazuun questline starts with Signs of the Wind and Land of the Apex at
/way #2023 41.6 56.7 Elder Nazuun (Signs of the Wind and Land of the Apex)