Irelia Runes explained
There's one set of runes for Irelia on patch
11.19
that is the clear favorite for LoL players and pros alike. The best Irelia Runes on the position 
Top are Precision as the primary path and
Resolve as the secondary path with a pick rate of 54%. Besides runes you should take a look on Irelia Build and if you are interested in pro matches take a look at Irelia Probuilds. If you want to discuss
Irelia then you should visit the champion subreddit.
Primary path on Irelia
Precision improves attack and sustained damage on Irelia troughout the match. Most of high elo players – and our LoL pros in the the major regions – have agreed that
Conqueror is the best keystone rune to run on
Irelia. This keystone rune provides additional power in the later stages of a game. As soon as
Conqueror is fully charged, Irelia deals additional damage and gains life steal. This is usually followed up by taking
Presence of Mind,
Legend: Alacrity and
Last Stand.
Presence of Mind helps Irelia with the mana problems by restoring missing mana, if a champion is killed.
Legend: Alacrity grants additional attack speed to Irelia. With
Last Stand you deal more damage while you are at low health.
Secondary path on Irelia
When it comes to your secondary path, most
Irelia players prefer to go with
Resolve.
Resolve empowers the survivability of Irelia and increases the tankiness. On the
Resolve path, the best runes for Irelia are
Unflinching and
Bone Plating.
Unflinching inceases Irelia tenacity based on your missing health.
Bone Plating make Irelia overall tankier, by decreasing the amount of poke damage in the early game.