Aurora vs Jax

Poke with Twofold Hex (Q), then recast it once the target has lost health: the hex passes back through them and deals more damage the more health they're missing.

Cast Across the Veil (W) to dodge a skillshot or break a chase: you leap and turn invisible briefly, and a takedown resets its cooldown.

Cast Between Worlds (R) in the middle of grouped enemies: those trying to enter or leave the area are slowed, which keeps them under your team's spells.

Inside Between Worlds (R), teleport from one edge to the other to dodge skillshots and reposition, as long as the area lasts.

Take a short trade, then back off: Relentless Assault (passive) increases his attack speed with each consecutive auto.

During Counter Strike (E), back off instead of attacking: he dodges your autos, then stuns nearby enemies, dealing more damage per dodged auto.

Trade right after Counter Strike (E): it's both his defense and his only stun, and it has a 17 to 9 second cooldown.

In the late game, don't leave his split push unanswered: send someone to hold his lane, or force an objective on the other side of the map.