A rune page for Kai'Sa reasoned from its class, range and damage type — with the thinking shown rather than a win-rate table.
Rune pages get copied far more often than they get understood, which is why they stop working the moment the matchup changes. Kai'Sa is a marksman whose job is to deal damage every second of a fight from behind people who can absorb one.
525 attack range means Kai'Sa wins by not being where the fight is. Spacing is the whole skill, not a detail of it.

Precision — Marksmen win by attacking for the whole fight rather than winning one exchange, so the keystone that rewards sustained attack speed fits the job description.
Attacking an enemy champion grants you Attack Speed, up to 6 stacks. At max stacks, deal bonus adaptive damage On-Attack.
Killing a target heals you.
Takedowns on enemies grant permanent Attack Speed.
Deal more damage to low health enemy champions.
A starting point reasoned from class and range, not a win-rate ranking. Matchups change it.
Take Killer Instinct at levels 6, 11 and 16 — the ultimate is always worth the point it costs.
For the basic abilities, Void Seeker (W) gains the most from being ranked: its cooldown falls by 6 seconds between rank 1 and max, which is the largest improvement in the kit. That is the usual argument for maxing it first.
This is reasoning from the cooldown data, not a win-rate ranking — a matchup that punishes you can invert it.
The page above assumes an even matchup. Against a lane that beats you up early, survivability runes buy you the levels you need; against one you outrange, damage runes compound the advantage.
Kai'Sa is mana-gated, which is the real limit on how often you can contest a wave early.
These are the designers' words, not ours — the tips shipped in the client for Kai'Sa.