Hey guys,
This is my first build and its the way i prefer to play veigar. I play him as a pure nuke mage with no defensive items, the way i see it is if you kill them first they cant kill you. xD

Pros
-Amazing late game
-Anti-Ap Mage
-Stun is key in team fights
-can pretty much 1v1 anyone
-Nuking power is unrivaled

Cons
-Quite squishy all game
-weak early game
-can be out-harrassed easily
-mana problems early game

Please read through the entire guide before voting. hope this helps some of you!

As for runes,

Greater Mark of Magic Penetration Greater Seal of Replenishment Greater Glyph of Cooldown Reduction Greater Quintessence of Ability Power

Veigar has some mana problems early game so the flat mana/5 seals gives him that little bit of mana he needs to stay in lane.
As for the Cooldown reduction runes, i also prefer the flat cooldown runes because combined with masteries that gives about 15% CDR at lvl 1 and that is extremely beneficial for when you are farming minions. However these can also be replaced with Flat or AP/lvl runes as well.

Marks are pretty standart mpen and witgh boots this pretty much makes most squishies have no MR early/mid game.

As for quints, AP is pretty standart for early game last hits in case you missjudge the last hits.

Standard caster mastery build, i dont get expanded mind because it doesn't make that much of a difference early game and late game he has no mana issues due to a stacked tear of the goddess and his passive. I prefer getting longer lasting buffs for maxing out CDR and keeping your ult CD under a minute.

Recommended:


Teleport:
I prefer this summoner spell because it lets you move around the map with ease and can be handy for a quick escape after you throw down your stun if your in alot of trouble. It also allows you to get back in your lane early game in case you get harrassed too much and have to go back often.


Flash:
Flash is a key summoner spell on Veigar, it allows you for a quick escape over a wall of just get out of range of someone like nunu's ult. Combined with your stun it allows veigar some nice escape from almost anyone. Or used offensively flash into range to land a stun then combo.

Other Possible options are:


Ghost:
This can be used as a substitute for flash or along side it to really gain some distance. Although i prefer flash it wouldn't be bad considering the bit lower cooldown on this spell.


Ignite:
Ignite is nice for a early/mid game kill, although i enjoy this skill on some heroes, veigar's combo late game will kill almost anyone with any need for ignite.


Clarity:
This will allow you to spend more time in lane early game but as soon as you get your tear this essentially becomes useless due to h is passive.

Baleful Strike: Single target damage spell that does 80/125/170/210/260 magic damage plus 60% (.6 ratio) of your current Ability Power as damage. Passive: Veigar gains 1 AP permanently from any last hitting any minion with Baleful Strike and a 1/2/3/4/5 AP permanently for last hitting any champion with a damaging ability.
This is your bread and butter skill, its fairly hard hitting and allows you to farm early game, it takes a while to judge how much hp the skill will do on minions for its first 2 levels but the extra 15-25 AP you get from runes will help that out alot. Thats why early game you have to focus on last hitting, you tend to get 60-100 extra AP. I usually have about 50-60 AP with runes before i get any AP items.

Dark Matter: AoE damage spell that deals 120/170/220/270/320 magic damage plus 100% (1 to 1 ratio) of your current Ability Power as damage after 1.2 seconds.
This is an amazing skill mid/late game, almost spamable aoe nuke, you can hit any of their carries for about half HP before the fight even begins, it also helps for destroying waves of minions pushing a tower, does alot of damage mid game too when its maxed, when this skill hits about level 4 you start spamming this into minions and heroes trying to weaken them for your full combo.

Event Horizon: Veigar's stun, when placed, anyone (champion or minion) who passes through its perimeters becomes stunned for 1.5/1.75/2/2.25/2.5 seconds.
This is a very nice stun, takes a bit to get used to. They have to touch the edge to be stunned. Try to face the outer edge of the stun towards them so that if you miss it they have another one to walk through. This AOE stun helps so much in team fights and allows you to pull off your combo. When it hits level 3 it will stun them long enough for you to land dark matter without having to guess where he might move to. It will get you so many kills and save your life so many times. One of the reasons why I get alot of CDR is for this skill to have a relatively short Cooldown.

Primordial Burst: Veigar's Ultimate. Veigar sends out a burst of damage to an enemy champion dealing 250/375/500 magic damage plus 120% (1 to 1.2 ratio) of your current Ability Power PLUS 80% of your target's Ability Power.
This skill is why everyone hates veigar and why i love him. It has an amazing AP ratio and does 80% of the targets AP extra damage. You pretty much 1 hit any caster late game with this skill. Its also why i tend to go the build i go. With over 800 AP with skill will hit 1.5k + 80% of the targets AP and max CDR will give it under a minute Cooldown. It does work on targets without ap though too, so dont feel the need to save it. It alot wrecks certain tanks like Galio.

Standard Combo
Event Horizon -> Dark matter -> Baleful Strike -> Primodial Burst -> Baleful Strike

Core Item Build:


To Play Nuke Veigar, you want the most AP possible so these 4 Items are key. The last 2 items are really dependant I always get the extra Archangel's Staff because the passive stacks and will really boost your AP. The last item is normally between Rylais Crystal Scepter and Zhonya's Hourglass. Normally i Get Rylais Crystal Scepter because it gives the little extra HP to survive and gives a slow to your skills. However when playing heroes that have a delayed or global ult or combo *****s such as Karthus, Vladimir, Ezreal, Veigar or Anivia, you want to get a Zhonya's Hourglass for the active.

Other Situational Items

A third Archangel's staff is a nice addition, it will probably give a bit more AP overall than Rylais but wont give the slow or HP, so its really a Toss-up.

Since this is a Nuke build i dont recommend this item however there are a few Heroes i would get this against, to gain an edge like another Veigar or LeBlanc.

/ A little bit of MPen isn't bad but I prefer the Straight up AP. but against MR stackers it might be better to get some Mpen but with boots and runes you usually have enough to take squishies down without trouble.

Alot of people like this item on veigar but i prefer Morello's Evil Tome because it gives the extra CDR and they are easily interchangable. I dont think the active gives that much extra unless its against a tank. Your standard combo can take down nearly any character in the game without it. I tend to only get Deathfire if they have 2 tanks or HP stackers like Singed.

Ah the famous Mejai's. Alot of people get this Item on veigar and i dont think it suits him. Unless your on a Roll theres really no point to getting it. You can max CDR with runes, masteries, Morello's and an elixir or blue buff and veigar isn't an early game champ therefore building up stacks would be hard to do early/mid game. Overall i like this item on some mages like LeBlanc but Veigar is best served by getting different items. HOWEVER, if you find yourself getting 5 kills by 15 minutes in, by all means grab one.

Early Game:
Regardless of if you have the solo lane or not, you wanna farm AP. I prefer a solo lane with veigar because it gives me the opportunity to last hit without having to share. I know this sounds selfish but last hitting early game is why he becomes to powerful mid game without too many items. Start with a Meki Pendant, a Health Potion and Mana Potion. Dont play aggessive last hit with baleful strike when you can or just an auto attack if its on Cooldown. Dont consistently auto attack or you will push your lane and be easy prey for a gank, specially if they have a jungler. Go back as soon as you have enough for a Tear of the Goddess to start building it up, if you get first blood, when you go back you might have enough to buy 1 level boots as well.

Mid Game:
By now you should be around level 9 or 10 and have some decent damage from farming and a Fiendish Codex or Morello's Evil Tome. Your stun is perfect for setting up ganks, so continue farming your lane until you see an opportunity for a gank in your lane or another, at this point if you have i solo lane i would suggest buying a couple wards for your bushes and maybe dragon if your jungler has not warded it already. At this point you can start harrassing the enemy well, you have enough mana to drop dark matters all over t he place and hit them once or twice, then when they have about half HP and you have enough mana, throw down a stun and lay em out. From then on they will be scared everytime you throw down a stun so you can use that to your advantage.

Late Game:
This is where you shine. You should at least have you Needlessly Large Rod and well on your way to a deathcap if you dont have it already, you can now burst down AP champs with ease and most carries too. Teamfights will be a regular occurrence now and your stun it key, you also tend to initiate by stunning one of the enemies that overextends. Throw down your combo then back off so you dont get focused when they get free of stun and repeat. Your team should constantly have baron and dragon warded and be sure to defend towers from waves of minions with your Dark Matter.

Thanks for reading my guide! Vote and comment please, i appreciate your feedback and I will be happy to answer any questions you have.