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Kassadin has multiple item paths; he can go caster via Mana and Ability Power or anti-caster with Cooldown Reduction and Magic Resist.
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Kassadin's ultimate has many uses and is on a shorter cooldown than most, use it often.
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Try to get the Ancient Golem buff to counteract Riftwalk's increasing Mana cost.
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Kassadin deals mostly magic damage. If he's doing well consider buying magic resist items like Mercury's Treads and Banshee's Veil.
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Each time Kassadin consecutively uses Riftwalk, he pays more and more mana. Keep this in mind as you chase him.
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It takes 6 spell casts for Kassadin's slow, Force Pulse, to become castable. If he levels up that ability, judiciously use your own skills while laning against him.