Pros:


Fun to play
Amazing burst
Infinite scaling
Easy to pick people off
Can sway a fight easily

Cons:


Squishy
Gets focused
No escape (other than stun)
Can have mana problems

Ignite - This is the best offensive summoner spell and can help you 100-0 someone with that extra damage. You could also take teleport instead of ignite for more mobility.

Flash - This is the best summoner spell for almost all champions and almost everybody gets it. It will let you chase people, get away, and dodge skillshots. This is a MUST summoner spell.

Crystalline Flask - Great sustain for early farming. In general use this before potions because you can refill it.

Doran's Ring - Good early when you have item slots to spare. Great gold efficiency for the stats.

Sorcerer's Shoes - Gives mobility and the mr penetration is great early when they have low mr.

Rabadon's Deathcap - This is your main damage item that almost all ap mages get. It is especially good on veigar because the passive scales with your q so every time you kill something you get 1.4 ap. Also you will be building plenty of ap later on and this will make it more effective.

Zhonya's Hourglass - Along with giving you a lot of ap, this item gives you one of the best actives in the game. The invulnerability is great when you are getting focused and you need your team to help you. Just pop the active and help will be on the way.

Void Staff - The passive of mr penetration is great for killing tanks with lots of mr because it is a percentage of their mr that is shredded. This item is also relatively low cost and gives you plenty of ap.

Deathfire Grasp - This item makes veigar's burst hit a lot harder. Use this item at the beginning of your combo for maximum damage output.

Athene's Unholy Grail - You will be one of the enemy's main targets late in the game, especially for the opposing ap carry, and this will help you survive a little longer. Also the mana regen it gives you is incredibly useful for long periods of not going back.

Veigar has the highest burst damage in the game(other than maybe Leblanc) and his abilities allow him to do this. This is also why veigar should really go in a solo lane, so he can level up his abilities.

Equilibrium - Veigar's passive allows him to get increased mana regen as his mana gets lower. This means to use it effectively you should wait until you are relatively low on mana before using a mana potion.

Baleful Strike - Veigar's q is his harass and farming tool. Last hitting with this gives you 1 AP(or 1.4 if you have rabadon's), but make sure you don't use it too much so that you run out of mana. You can use this after level 6(or before) to harass until they are low enough to kill with one combo. You want to max this first.

Dark Matter - This ability adds a lot of power to veigar's burst later in the game. It scales very well with AP and not as much with leveling it up, so you don't have to get to many points in it early. Try maxing it after your stun(e) is long enough to keep them under the dark matter. You can use this ability after you stun for damage or in a bush for vision since it reveals before it hits.

Event Horizon - This ability starts veigar's combo. It makes a circle which when people touch they get stunned so try to put the edge right on top of the person. This is the only ability you should not put on smart cast because it makes the circle around the mouse and you won't know the exact range around. You want to max this second until you think it is long enough(usually level 3 or 4) to land your w afterwards.

Primordial Burst - Veigar's ult has the highest single target damage potential in the game. It scales off of both your ap and the target's ap. This makes you want to generally use it on the enemy ap carry. You can also use it on others later in the game when your ap is high.

Combos:

General combo - Event Horizon -> Dark Matter -> Baleful Strike -> Primordial Burst (if needed) -> Ignite (if needed)

All in combo - Baleful Strike -> Event Horizon -> Dark Matter -> Primordial Burst -> Baleful Strike -> Ignite (if needed)

Finishing off combo - Baleful Strike -> Primordial Burst

I think veigar is a great champion and is very enjoyable to play. When he gets fed he just kills anyone whenever he wants to and when he isn't he still has play making potential. Veigar is also a great first champion to play because he allows you to learn how to farm, stay in position, and use combos. Finally, veigar is not too popular so you can surprise your opponents with your burst and unique play style. I hope you liked my guide and I will make sure to keep adding chapters about runes, masteries, strategy, and different phases of the game.

BYE!