Karthus Runes explained
There's one set of runes for Karthus on patch
11.19
that is the clear favorite for LoL players and pros alike. The best Karthus Runes on the position 
Jungle are Domination as the primary path and
Precision as the secondary path with a pick rate of 84%. Besides runes you should take a look on Karthus Build and if you are interested in pro matches take a look at Karthus Probuilds. If you want to discuss
Karthus then you should visit the champion subreddit.
Primary path on Karthus
Domination improves burst damage and assassination tools on Karthus. Most of high elo players – and our LoL pros in the the major regions – have agreed that
Dark Harvest is the best keystone rune to run on
Karthus. This keystone rune gives you additional damage throughout the match. This is usually followed up by taking
Cheap Shot,
Eyeball Collection and
Ravenous Hunter.
Cheap Shot makes you deal more damage to enemies with impaired movement, which has great synergy with the setup of Karthus.
Eyeball Collection is next up. This grants the user additional damage with every killing they score.
Ravenous Hunter is the final rune of the
Domination path. This rune gives some survivability during short fights and damage trades during the laning phase. The additional health is nothing to scoff at and can mean the difference between winning or losing a battle.
Secondary path on Karthus
When it comes to your secondary path, most
Karthus players prefer to go with
Precision.
Precision improves attack and sustained damage on Karthus troughout the match. On the
Precision path, the best runes for Karthus are
Presence of Mind and
Coup de Grace.
Presence of Mind helps Karthus with the mana problems by restoring missing mana, if a champion is killed. Karthus deals with
Coup de Grace more damage to targets with low health.