Deal 7% more damage to low health champions. Gain AD/AP after kills or assists.
Kassadin's strong slows on [E] makes Comet incredibly reliable to land for that extra lane harass damage.
WhyThe Ultimate Hat
Thanks to the already short cooldown on Kassadin's [R], he is able to get full Ultimate Hat stacks very quickly. This lets you take a few extra Riftwalks in the mid game for chasing kills/escaping, where you other wise not be able to.
Celerity on Kassadin allows you to keep up with and stick to your opponent when you're running them down in an all-in.
Scorch is a rune that, like Aery, is very strong and reliable during lane. These two combined make for a strong poking tool with [Q].
If you're looking to scale into a longer game rather than harass in lane, Gathering Storm is a decent option here.
WhyPresence of Mind
Presence of Mind is a fantastic rune choice on Kassadin as it allows you to repeatedly [R] after leveling up or getting a kill/assist in teamfights, building up and ramping your damage incredibly.
WhyCoup De Grace
Coup De Grace is the most reliable damage amp rune for Kassasdin, especially when you're able to stick to the back-line enemies and blow them up with [R].