I think you might find a few answers here
Of course Astrology is not the only magical science used by Sharlayan. I would wager that they actually tend to integrate every kind of magic there is to learn.
But for stuff directly originating from them, yeah, astrology for sure, probably poroggos (unless it's specific to Matoya), and possibly magicked brooms (that are seen all across Eorzea).
Seeing the kind of spells Y'shtola or even Louisoix seem to cast, they seem to have access to very powerful magicks.
Of course Astrology is not the only magical science used by Sharlayan. I would wager that they actually tend to integrate every kind of magic there is to learn.
But for stuff directly originating from them, yeah, astrology for sure, probably poroggos (unless it's specific to Matoya), and possibly magicked brooms (that are seen all across Eorzea).
Seeing the kind of spells Y'shtola or even Louisoix seem to cast, they seem to have access to very powerful magicks.
Balmung:Â Suen Shyu