This Build is made so that Veigar can still be his high damage self but yet more durable, and that allows him to stay in his lanes for longer which rely's on last hitting minions with your Baleful Strike. I personally like to get at least 55 ap with it before i recall, because this allows me to get the ap items/boost that will make you a huge threat early on, because you can take a little bit more damage then your enmies expect and can be the same old "Droppin Nukes Veigar"

The reason why you should get Baleful Strike as you're first ability, is because you have to last hit minions in your lane to get an early ap boost against your enemies, also this spell does good damage against target champions. (when you kill a unit with Baleful Strike Veigar can gain 1 ap at lvl 1,up to 5 ap when at lvl 5 so try to last hit any target with Baleful Strike to get extra ap.) This spell also costs very little mana so combined with your mana regen seals you dont have to worry about using it too much.

I like to get Event Horizen 2nd because it will help aton when you are chasing enemies and running away from them , because of it's major stun effect allows you to stop enemies that are running away and which allows you to take them down, and when you are running away it is great to put down infront of enemies to make an excape. This is incredibly useful in combination with your other spells, because when you have all of your abilities, you can initiate with your Event Horizon then drop your Dark Matter where the enemy is stunned, and then follow up with your Baleful Strike and Ultimate, this is an assured kill against bacically anyone except for huge magic resist tanks.

Dark Matter is an incredibly strong spell late game by being able to drop half/quarter of a target champions health if you get the proper items. Dark matter is a tricky spell to use without Event Horizon though, because it takes time for it to hit the ground, that is why you use it with Event Horizon where the enemies get stunned and is an easy terget for Dark Matter. The reason why I personnaly dont get Dark Matter to early in the game is because it is to heavy on mana. So around mid/late game is when i use darkmatter the most because then is where i have my ap and enough mana to fully complete a nuke that will kill an enemy.

Greater Seal of Replenishment: The reason for this Seal is because veigar is a very heavy mana costing champion so i like to have good mana regen to be able to stay in lnes longer and harras alot more.

Greater Mark of Insight: The reason why I get this Mark is because it is really benificial when ur against any champion because the spell pen. allows you to do alot more damage then they would expect wich will lead into lots of kills, because when you nuke with veigar having extra spell pen. is giving you an extra chance for a kill.

Greater Glyph of Focus: The reason for this ap cooldown glyph is to help you all game round with veigar, because his abbilities do not have very short cooldowns so i personally like to be able to put my spells up alot quicker then later. An example of that is when you're chasing an enemy champion, you really want you're Event Horizon up, but you probably used it to nuke, so having it uo quicker is great to catch the enemy again with it.

Greater Quintessence of Fortitude: The reason behind having this flat health Quintessence is to make veigar alot more durable in early game fazes. By being able to stay in lanes a lot longer, which allows you to get more last hits so when you recall you can get you're items quicker.

Ignite: The reason for ignite is to help you all game round, because early game it is great to have ignite in combo with your abilities, because early game nuking with veigar gets enemy Champions very low health, so one ignite and their dead. Late game ignite as you all know does great damage, so using it in combo with your abilities is great... (and it is great for killstealing :P)

Ghost: The reason for ghost is because early game it is great to catch up to Champions that are weak/running away with ghost, and then to be able to put down Event Horizon and finishe them off. Also it is great for getting away in combo with Event Horizon because if you are being chased, you just put down you're Event Horizon and pop out ghost for a smooth get away.

Veigar is a great famer late game because of his Dark matter, late game your Dark Matter should 1 hit the minion trio's which is great for the extra gold. Also a good tip with veigar is that when you have good ap and Dark Matter is lvl'd up you can just put your Dark Matter in the middle of the Ghost Camp which will take them all out and give you and effortless $100