You have received an unexpected invitation and hasten to the Astrologicum.
This quest is available if you have completed the quest Litany of Peace.
Starting the Quest
Talk to the House Fortemps Knight outside of House Fortemps in Ishgard to begin the quest.
Speak with the House Borel Steward
Use the Aethernet Shard to go to the Athenaeum Astrologicum Aethernet Shard and go east to where the orange arrow is pointing in the minimap. Talk to the House Borel Steward. There will be a cutscene.
Return to Fortemps Manor
Talk to the House Fortemps Guard and say Yes to enter Fortemps Manor. There will be a cutscene. This one is important, so it is recommended to watch it either now or via the Unending Journey in an inn room.
Speak with Alphinaud
Talk to Alphinaud to complete the quest.
Next Main Scenario Quest
After you complete the quest, talk to Alphinaud to accept the next quest: Shadows of the First. There will be a cutscene.