Greetings, I am a rather new player to League of Legends having just hit thirty today. This is my first guide so I am sorry if it is difficult to understand or flawed in some way. My experience with the game is mostly with Cho'gath who is my main, but have played many matches recently with Veigar and have come to understand him to a degree. From my personal experience Veigar has to be played very carefully, but if done right and you enter end game without being farmed, then you have an unstoppable nuke in your hands.

I chose to go with 21/0/9 as my build because of the addition of the Ionian boots to the game. By not going 9/0/21, you gain 12% critical strike chance, 10 ap on ignite cd, 4% faster normal attack rate, and 5% more damage while losing 5% experience gain, 3% movement speed, and 21% cdr.

The 5% damage increase should speak for itself, but the value of 4% faster normal attack rate and 12% critical strike chance might confuse some. None of Veigar's abilities work on buildings so you are stuck with the same old slow autoattack when tearing them down. As for late game, if the game lasts long enough for you to get Lich's Bane then you will see what makes these stats so important. Your autoattack after your combo with your AP added to it will be built into your rotation and with it hitting some 1k+, critting will add a tremendous boost.

Veigar normally will be taking middle so the experience loss doesn't impact you much. The loss of 21% cdr is easily replacable with the new boots that give 15% cdr. Those, along with blue buff or maxed mejia's soulstealer and a potion of brilliance will instantly give you cdr cap of 40%. The movement speed is probably the greatest loss you will notice but even that isn't too influential as veigar won't be doing a lot of chasing; if you attack someone, they generally die before they can get away.

Ignite

With your masteries you will gain 10 AP when ignite is on CD. That is a rather large effect early game as it allows you to use ignite to whittle away their HP and gain a buff while it is on CD. That means it is never truly going to waste whenever you decide to weaken someone.

Exhaust

Exhaust, paired with ignite, will make harrassing a player a joke. In addition to the normal effects of exhaust it will also reduce their magic resistance by 10.

Add these two abilities together and you are able to slow the enemy, weaken them, inflict a nice chunk of damage outside of your rotation, and strengthen yourself for the burst.

Greater Mark of Insight

9 of these will give you 8.55 Magic Penetration. Magic penetration is extremely important to Veigar as it is what will bring tanks to kneel at his knees (not an easy task, I tell you). End game Veigar can hit 3-4k damage instantly with his rotation, but if 60% of that is removed then you're only doing 1.2k-1.6k.

Greater Glyph of Potency

Greater Seal of Potency

Greater Quintessence of Potency

Now looking at these, you may be asking yourself "why not go for some cdr or some more magic pen? Surely these won't have much impact end game when Veigar has over 800 AP". The reasoning behind this is for the sake of being competitive early game. Veigar is less than impressive early game and it can be quite hard to hold your own in mid or to help a partner push a side lane. Between these runes and ignite you will begin the game with 38.67 AP.

Start out with Meki's Pendant for the mana regeneration. You may choose to purchase a health pot or two as well depending on personal choice, but if you are careful with Veigar then you shouldn't need any. Try to take middle if you can, but if you are forced to lane then try to choose one with a tank or toughie. Farm minions initially making sure to get the last hit with Baleful Strike as often as possible to increase your AP. Try to avoid confrontation with the opposing champions to maximize your income in the lane and your AP growth via Baleful Strike. Once you be BS to level 2 or 3, start harassing the enemy champion to push pressure on them and keep them from playing too aggressively. Whenever you hit 600g you should recall and pick up your Tear of the Goddess. Return to your lane and continue as you have been.

Your aim on your second time in the lane is to walk away with 900g. It is alright to stay past that point if you can handle the pressure from the other champ or if you are pushing them back, but try to at least hit this amount. By this time your mana pool should be reaching the point of being endless (from the combination of your own % mana regen and the tear of the goddess increasing your max mana) so buy your Ionian boots for the 15% cdr. With your mana being self sustainable you don't have to worry about casting too frequently so let loose with your Dark matter and even the occasional Event Horizion/DM/BS on the opposing champ if they let you.

Your income should be pretty fast so at this point your choice differs based on how the game is progressing. If your team is managing lots of kills then head back as soon as you have the 1235g for a Mejias, but if the game has been pretty slow or your team is actually the ones being wrecked, stay and save up 1860g to finish your Archangel's Staff. Either way you will complete Mjias right before or after your Archangel's Staff as Veigar can gain assists just from throwing your barrier around the opposing team and by this point Veigar should be able to blow holes in the other team.

Until Mejias gets fully built, you should aim to always have blue buff. That will keep you at max cdr which is essential due to the long cd of Event Horizon and your ult.

Play it safe and keep farming the minions. Don't get greedy or overconfident and chase an enemy with no HP. Veigar won't be able to dominate until you get Rabadon's Deathcap, and even then you won't be able to finish the stronger champs until Lich's Bane.

If all goes well throughout the game you should have over 1k AP and 48.5 (58.5 if exhaust is on them) magic penetration. Your ultimate should one shot any caster champion and your full combo should instant kill just about any other champion. You must still be careful as they can probably 2-3 shot you themselves, but with a good tank you will absolutely mow through their forces.

Your skill rotation in any assault should be Event Horizion so that the edge touches them-> Dark Matter -> Exhaust -> Baleful Strike -> Primordial Dust. Event Horizon traps with the edges of the prism so try to land the edge right on them, then cast Dark Matter immediately so it'll hit before they can get away. Next you want exhaust on them in case they have Mercury Treads or any other stun reducing effect and for the -10 magic resistance. Finally your Baleful Strike followed up with Primordial Dust should leave them as a twitching pile on the ground. Don't forget to stay on them afterwards though in case they do barely live or they manage to get out of the Dark Matter. Your autoattack, while slow, is actually pretty powerful mid to end game hitting for 300s before you get Lich Bane.

Veigar is an extremely powerful champion who can either capture and obliterate his opponent or stun multiple enemies in their tracks and save his teammates from what would be certain death. He can become an unstoppable nuke whether or not you played well beginning game so never give up with him.

I hope you have found this guide informative and helpful and I am eager to hear how others performed while trying it out. Good luck and have fun.