This is a very helpful AP Xerath build to help you stay back and shoot lightning at people, i hope this guide helps you and it makes your enemies wonder what just happend.

Ascended Form is his passive, 15% of Xerath's Ability power turns into armor, so try to get as much AP as possible.
Arcanopulse is his Q, it shoots a line of lightning the direction of your choise, best used after you use Mage Chains so arcanopulse will stun the enemy for a few seconds.
Locus of Power is his W and it gives you magic penetration and a ton of range for a few seconds but you arent allowed to move unless toggled off, so it is best used in team fights.
Mage Chains is his E and you throw a ball of lightning at the target that does high damage, then his next spell will stun the enemy, so it is best used first in a fight.
Arcane Barrage is his R and it can be used 3 times in 12 seconds, it is similar to leona's ult, they both shoot a beam from the sky in an area for high damage but Xerath's doesnt stun them unless you hit them with Mage Chains first.