Hello everyone, and welcome to my Veigar Guide. This is MY way of playing Veigar, and it will NOT work for everyone. This guide maximizes late game AP, for some heavy nukes. However, the lack of survivability items can make Veigar much more difficult to play. But this is where the challenge comes in, doesn't it feel good to ace the other team while gaining 2-4 kills and assists and surviving? I've been playing Veigar for a long time, and tried many builds but this is my favorite. Another thins is please try the build before voting/commenting, and feel free to ask questions
NOTE:This build can be changed situationally, and to personal preference.

Pros

-Great farmer
-Insane late game nuke
- Lich Bane's passive add's an extra burst to your combo, and owns turrents
-Stun can be a real life saver, and great help to your team
-Ultimate scales with 80% of target's AP, making them an easy nuke
-Tons of mana and mana regen late game

Cons

-Squishy
-Usually focused first
-Can be hard to play and nuke properly
-Mana-hungry early game

x9 These help make your early game harass much better, and work well throughout the entire match as enemies begin to get more MR.

x9greater seal of vitality Half the price of flat HP seals while giving almost 4x the HP. I take these to help combat Veigar's squishiness. Another alternative could be dodge seals

x9 These give more late game AP than the flats The flats are not bad it is up to personal preference, and I would not recommend any other glyphs for Veigar.

x3 Probably the best quintessences for any AP character. Another alternative can be flat HP quintessences if you feel you need the extra HP.

Recommended Spells

Flash Probably my favorite summoner spell in the game. This spell can be used as a great escape, giving you the ability to flash through walls or away from enemies. This spell can also be used offensively to catch up to an enemy.

Ghost Can be used to return to lanes faster, run away from enemy champions and also catch up to them. Combined with flash you almost have a full proof escape.

Ignite Great spell to have against champions with healing abilities, or stacking spell vamp and life steal. This spell is also great for getting that last hit on runners.NOTE:Keep in mind this spell does true damage.

Exhaust First off if you take this replace the mastery point in Deadliness for a point in Cripple. This spell can really change the course of a fight, rendering a target pretty much useless. Another way to use this is to slow the target making them easier to chase.NOTE:Try to use this spell on AD characters rather than AP characters.

Teleport Great for those, "I need to be there right ****ing now" moments. Can also give you a great advantage in lanes allowing you to lose almost no time when returning to your base.NOTE:This spell teleports to minions, towers, wards, and other champion skills such as Teemo's shrooms and Shaco's boxes.

Cleanse This spell works well against high CC teams, it removes ALL debuffs from your character and shortens the duration of incoming ones.

Not Recommended Spells

Heal Although early game it can be somewhat useful, to me 100-300 HP will not save your life with how squishy Veigar is.

Clarity This spell is only useful early game up until you have your tear. With this build you will have a ton of mana and mana regen, making this spell useless late game.

Fortify Save this for the supports.

Clairvoyance Once again this spell is mainly for support characters and I would not recommend it for Veigar.

Revive If you really want an extra life just build a Guardian. This spell is not worth it due to its high CD.

Rally 15 seconds of 10 AD will do nothing for you...

Smite This is only good for junglers. I mean if you are really that bad at last hitting I guess you could take it...

Archmage's Savvy Putting the 3 full points in this offensive mastery synergizes well with the scaling AP Glyphs, giving an extra 10.8 AP at level 18

Sorcery Taking 4 points in this gives 3% CDR on all of your champions abilities, it also allows you to take the next mastery.

Archaic Knowledge For 1 mastery point, getting 15% magic penetration is pretty nice. This works well with the magic penetration runes, giving you a great early game harass.

Haste I tend to always take ghost with Veigar, so improving the spell is worth the mastery point

Awareness Taking 4 points in this mastery can give you an advantage over other champions that do not. Leveling slightly faster than them can give you a nice edge, or being able to stay at the same level with those who take this mastery.

Expanded Mind Taking all 4 points in this mastery increases your max mana by 5% This mastery is good for this build to help increase the AP given from Archangel's.

Meditation Taking 3 points in this mastery will give you an extra 3 mana per 5 seconds. This mastery combined with Veigar's passive will give you the needed mana regen to farm with your Baleful Strike.

Greed This can give you a gold advantage over others. Also works good for those times you are only a little away from an item and decide to wait, decreases the loss of laning time.

Blink of an Eye Since you should be taking flash, reduces its cooldown is worth it.

Intelligence Taking 3 points in this mastery gives another 6% CDR, combined with Sorcercy you have a total of 9% CDR which is not too bad.

Presence of the Master Reduces the cooldown of your summoner spells by 15% allowing you to use them for frequently.

Doran's Ring A great item to start off with. This will give you the extra mana regen to help you farm more efficiently with Baleful Strike. The extra 100 HP makes you not as squishy early game while thegreater seal of vitalityHP runes start to kick in. The 15 AP simply makes last hitting a whole lot easier.

Tear of the Goddess This item should be bought on your first trip back, simply to start charging it up sooner. Continue farming with your Baleful Strike to charge up your mana and AP for late game.

Sorcerer's Shoes These are probably the best boots for Veigar. The 20 magic penetration will be useful throughout the game. Another alternative to high CC teams is Mercury's Threads.

Rabadon's Deathcap Probably the best item in the game for any AP character because of it's passive and huge amount of flat AP. The 155 AP boost is amazing, while your AP becomes increased by 30% At this point your full combo should be able to nuke almost anyone on the enemy team.

Archangel's Staff Built from the tear purchased earlier. Upon purchasing this item you should notice a significant boost in your AP. You should pretty much be able to lane almost forever without running out of mana at this point.

Lich Bane The flat 80 AP will scale nicely with the Rabadon's passive. The mana bonus will scale with your Archangel's. The 30 MR will give you a tiny bit of survivability. But what really makes this item, is its passive. Upon using an ability your next basic attack will do 100% of your AP in magic damage, with a small 3 second cooldown. If you manage to finish the full build in this guide this item is just insane. You should have around 1200+ AP and this item should be doing around a 1k damage auto attack.

Finishing the Build

Okay so after you have your few core items Sorcerer's Shoes, Rabadon's Deathcap, Archangel's Staff, and Lich Bane you have 2 more open item slots. A few suggestions are listed below.

x2 Archangel's Staff Getting two more of these is MY favorite. You just simply have an amazing amount of AP and by this time in the game the enemy team should either be stacking loads of MR just for you or QQing and calling you OP. If they stack MR I would highly recommend the item listed below.

Void Staff The 70 AP is just a bonus to this item's passive. The 40% magic penetration combined with Archaic Knowledge gives you a total of 55% magic penetration, so you should be shredding through tanks.

Abyssal Scepter This item gives you 70AP increasing your nuke. The 57 MR will help your survivability. The aura this item gives, reduces the MR of nearby enemy champions by 20. This item is good as enemies begin to stack some MR.

Deathfire Grasp The 60 AP increases your damage output. The mana regen allows you to lane longer, and the passive reduces your cooldowns by 15% This combined with Sorcery and Intelligence will give you a total of 24% CDR. What makes this item really great is its active. It deals magic damage equal to 30% of the targets current health, increasing 3.5% per 100 AP. This will give you an insane burst and combined with your ultimate there is almost no way for an enemy to survive.

Rylai's Crystal Scepter If you feel you need the extra HP this item is higly recommended. This item will give you an extra 500 HP, greatly increasing your survivability. The 80 AP increases your damage output, while the passive causes your abilities to slow the target.

Rod of Ages First of if your going to get this item, it should be built before Rabadon's and after your tear. This is because you want enough time to fully charge the Rod, to maximize its capabilities. This item is also if you feel you need the extra survivability. Fully charged this item gives 630 HP which will allow you tank a couple more hits. The 725 mana will increase your AP because of Archangel's Staff. The 80 AP as said several times about the other items, will increase your damage output.

Zhonya's Hourglass The flat 100 AP scales well with Rabadon's. The 50 armor will increase your survivability. The active, places you in a stasis for 2 seconds, rendering you invulnerable and untargetable but unable to take any actions. This can allow you to wait out a cooldown for a spell, or if focused in a team fight allow your team to initiate and get there attention.

Will of the Ancients This is a great team item. The aura gives nearby champions 30 AP and 25% spell vamp. The spell vamp can allow you to lane longer and survive longer in team fights.

Banshee's Veil The mana from this item will scale with Archangel's Staff. The HP and MR give you more survivability. And the passive blocks one negative spell every 45 seconds which can come in handy quite often.

As I mentioned earlier you might be asking what's so important about farming with Baleful Strike? Well know I'll let you know. Whenever you last hit a minion with this ability you gain 1 AP permanently. This is what makes Veigar such a great nuker. If you can farm properly with Baleful Strike you will be surprised with the amount of AP you have.

Equilibrium This is Veigar's passive, it increases your mana regeneration by 0.75% per 1% of mana missing. This will allow you to farm with your Baleful Strike early game without going OOM(Out of Mana) every other minute.

Baleful Strike This is what really makes Veigar an amazing nuker. With this ability whenever you last hit a minion you permanently gain 1 AP. Also when you kill a champion with any of Veigar's abilities you gain 1/2/3/4/5 AP depending on the rank of this skill. This skill allows you to still have a decent amount of AP while saving up for your core items.

Dark Matter After 1.2 seconds dark matter falls from the sky dealing AoE damage. This spell scales with 100% of your AP. Once this skill is maxed it can be used as a great farming tool, and also dealing insane damage to enemy champions.

Event Horizon This is an AoE stun. It only stuns enemies who pass through the edges of the barrier.NOTE:They can still move inside the stun as long as they do not touch the edges of the barrier. This is what sets up for your nukes. Learning how to use this skill properly is key to mastering Veigar.

Primordial Burst This is Veigar's ultimate, otherwise known as any AP characters worst nightmare. It deals a base magic damage and scales with 100% of your AP. This ability also scaled with 80% of the targets AP, which is what makes this skill so deadly.

I take 3 points in Baleful Strike while placing 1 point in Event Horizon and Dark Matter.I then max Dark Matter while taking Veigar's ultimate Primordial Burst whenever it is available. I then max Baleful Strike and last but not least Event Horizon.
NOTE:Some people might say it is not possible or it is very hard to land Veigar's combo with only 1 point in Event Horizon. It may be hard but it IS possible. If you feel the stun does not last long enough you can take another point in it.

Now I will explain Veigar's skill order for how to properly nuke an enemy.

First, stun the enemy with your Event Horizon
Then, throw a Dark Matter onto the enemy champion.NOTE:Lower levels of Event Horizon will not stun the target for to long so try to aim a little ahead of the enemy, where they are going to try and run.
After, hit your enemy with a Baleful Strike
Finally, (if they aren't already dead) finish them off with your ultimate, Primordial Burst

Thanks to everyone who read the guide and made it to this point. I hope this helped you and remember the build can be changed to your liking to make it YOUR build. Remember this is just a guide and not a written set of laws on how to play Veigar. Veigar can be played many ways with different builds. This is my first guide so feedback/constructive criticism would be appreciated.