Everyone who plays veigar knows that he needs ability power. I'm opting for that, but also for a lot of magic penetration.
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Summoner Spells

Clarity - At the beginning, Veigar is EXTREMELY mana hungry, especially as I get dark matter first.

Heal - Veigar is squishy. Do I need to explain?
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Mastery Tree

As I just said, Veigar is squishy. That's why I have 21 in defense instead of offense or utility. For Veigar, the offense I chose is pretty standard for a caster.
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Skill Sequence

Many people choose Baleful Strike for your first priority. I say, yes, it is a good spell. However, I max out Dark Matter first, and let me tell you why. If you can nab mid, by level 9 you will be able to farm the wraiths in one shot without even going into the jungle. CHA-CHING!!! Free gold and exp with one spell.
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Rune Build

I got mostly magic piercing runes, which is what this build is about. The ability power helps with Veigar's ultimate ability, as everyone knows. The cool thing is, Veigar's 3rd ability also uses 100% of his AP. SWEET!
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Item Sequence

At the beginning, Veigar is very mana hungry. Even with clarity and a Meki Pendant, the mana potion is still needed. Sorcerers Shoes don't really need explaining - mostly any caster should get them. The Chalice of Harmony helps sate Veigar's thirst for mana, and it gives some magic resist, which is often handy in the mid. The void staff gives more magic penetration plus AP, a good item for MagicResist tanks. Once you have Lich Bane, you are ready to roll. With enough ability power, it does as much damage as your first ability. Hextech Revolver's spell vamp allows you to stay in the lane almost indefinitely just by using dark matter to one-hit minions. If you ever get enough money to buy Rabadon's, you suddenly go up another notch in damage, although it isn't needed to kill someone.
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I don't claim to be an expert on Veigar, but I hope you like this build. Any positive comments are welcome. =D

|!^3 German Squirrel