Nashor and Lifesteal don't do anything for him.
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You need to build AP since you're an assassin, you need high amounts of it. Nashors costs too much since it gives ASPD and CDR, and the passive, which are generally useless stats on Kassadin
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Since you're not building AD, you don't need Lifesteal
Lifesteal scales with physical damage, not magical damage.
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You need survivability since when you go to engage on someone, you're going to need to survive for more than 2 seconds so you can escape
Try this build, in order, for the most part:
Start> Flask + 3 HP Pots (These help you survive the early laning phase, since Kassadin is generally very weak and prone to harass here)
1st Item> Rod of Ages (Core) - Kassadin needs Damage and survivability, as well as some mana to be mobile. This is the perfect item.
Boots> Sorc Shoes or Mercury Treads (but almost always Sorc Shoes, Mercury Treads in a few exceptions where teams have an abnormal amount of magic damage and cc)
2nd Item> Zhonya's Hourglass (Core) - Kassadin is already resilient to magic damage because of his passive and his Q, therefor the armor here makes him a little tankier when being focused by ADs, and the active of Zhonya's is one of the best actives in the entire game.
Voidstaff - Blows through magic resist, pretty good item.
Deathcap - Blows through champions, pretty good item.
Guardian Angel - Just in case, 6 item Kassadin already does a ton of damage and usually if the enemy team sees a 6 item Kassadin with a GA, sometimes they don't even want to focus you, but they have to, because you're a 6 item Kassadin, obviously.
I'm a D1/Master mid laner and this is the build I personally use on Kassadin