Ok.
First out of the gate, Kassadin suffers from a number of constraints on his abilities due to his theme of being an "anti-mage" - either in paying power space for or having additional constraints:
a flat 15% reduction on magic damage
an antimagic shield
requiring multiple nearby spell casts to use his force pulse
While most assassins and mages have a spammable primary attack ability (that is, an ability which is on a shorter cooldown that they can use as a bread and butter offense/harass tool) Kassadin does not - he has a spammable mobility ability. This means that he can jump around a lot, but can't actually do a lot, because even if he jumps multiple times, none of his offensive abilities are available which really only allows itself for a jump-in-cast-everything-jump-out style of play. What makes this especially heinous is that his mobility ability scales quadratically in cost, so using his only spammable ability is highly punitive.
All of this would be fine if Kassadin had the burst or utility to support this kind of jump in burst jump out type of playstyle... but he doesn't. Kassadin will do support level damage until he has about 3 items, and then he will do fighter level damage until the item cap, where other assassins will be out damaging him far earlier in the game: Kassadin has decentish ratio's, but he lacks the steroids or conditional damages common to other assassins, and his base damages are all support level - Nami, Leona, and Sona will all out damage Kassadin for the first half of the game through sheer base damage, while having okay scaling on their abilities.
For Kassadin to be effective he needs to do much more damage, actual assassin level damage. What I propose is:
Q - Shield removed, AP ratio lowered to 50%, Target hit is now marked with "Void Resonance". Hitting an enemy marked with Void Resonance with a melee attack consumes the mark and does 20/40/60/80/100 (+30% AP) damage
This change will remove a bit of damage from Kassadin solely using his Q to poke, while it rewards a Kassadin who engages with melee on his opponent.
W - Cooldown reduced to 6 from 9
Since this ability puts him in harms way, it makes sense for it to have a shorter cooldown - this makes this Kassadin's primary offensive ability, so he can poke more often
E - Slow reduced to 50% at max rank, duration increased to 2.5 seconds at max rank, 20% of enemy's AP added to damage
Kassadin's current force pulse simply is not good enough to require stacks. The slow will allow him to stick to his enemy while the damage will be increased against his designated foe, mages
R - Cooldown increased to 9/8/7 ranged increased to 700
Simply put, this ability is the reason Kassadin is so weak right now. Since he functions as a burst assassin, it doesn't make sense for him to have a 2 second at max rank cooldown on this ability, since the costs placed on it reinforce the concept that you SHOULDN'T spam this. The problem is his old kit was so weak that he needed to spam this in order to even keep up with and finish off his prey - now that his overall combat effectiveness is increased he doesn't need a high-spam ultimate
These are the changes I would make to him, and would let him be an assassin again.
