Hi my name is idoc11, main veigar from eune, and I just wanted to share with you the build I came up with to veigar. It all started by that I wanted to see how full magic penetration veigar would work and it worked perfectly a lot better than all the morellonomicon and ludens builds so I stayed with this build for a while and I finally decided to share it with the LoL community.
I have calculated and a champion with 50 magic resist at level 18 for veigar will have 0 magic resist, an adc who won't buy magic resist will probably have less than 50 and anyone with less than 50 will have negative magic resist meaning they will take even more damage than what the ability damage is, this is why this build is so fun.

You take aery for the poke in lane, you can take either nullifying orb or manaflow band depends if the enemies have ap based team, transcendence for the extra cdr early and ap later, and scorch for lane poke.
secondary is resolve for being tanky as veigar got a lot of damage anyway because of his passive, bone plating helps a lot in lane vs pokers and conditioning makes you a lot more tanky since you are building resistances.

Getting the tear of the goddess to stack mana to be able to spam abilities and upgrade it to the archangel's staff for the ap and later for the shield from the seraph's embrace after that the abyssal mask is good for some magic resist and some more damage around you, which also helps your team, the sorcerer's shoes you should get in between its better if you would get it around the same time as the abyssal mask, but you should get the base boots a lot earlier. After that, the thornmail makes you a lot stronger since you get more hp and armor and the attackers take some damage back, but if you are in a condition vs no auto attackers and heavy ap based team, you can buy spirit visage instead. warmogs gives you a lot more hp and if you buy it as fifth item, you will have 3000 hp already and you will get the regen, so you become extremly tanky and you still got damage from passive ap. The rabadon's deathcap is a good item to complete the build, since by now, you stacked your passive nicely and the rabadons passive will take advantage of that and will make you do crazy damage while still being tanky from your other items. And the elexir of sorcery after you finished buying all the items.
If you face strong ap mid champion you should buy negatron cloak pretty early on it will give you 15% reduced magic damage.

When you ingage a 1v1 you should start with E if you hit it (you should) W then Q and after 0.5 seconds use ult as well. Don't use your ult as soon as you start the combo because you want your W to hit the target before your ult hits so your ult will deal more execute damage. In team fights use your E well, try to hit as many champions as you can or capture them inside your E. when you see a good chance after someone got stunned by your E or a few people together try to hit as many of them with your W followed by your Q and use your ultimate on a low hp target which is currently not dying to your team mates. If you already reached full build, if the target is squishy like adc or not a tank support or squishy mid laner your ult will kill them even if they are on 75% hp, and your W might even straight up kill them in one ability.

Pros
-you one shot everyone not matter who it is and how tanky he is with your full build and an average amount of stacks.
-you got a good amound of armor and magic resist
-you wont have mana problems at all you wont even need blue buff
Cons
-You are not getting 40% cdr as after the new veigar W buff for cd for more stacks, your W cd is already extremely low and veigar's abilities cd overall are pretty short.

When you farm try to get 2 minions next to each other and making both of them low on hp so your Q will hit both and kill both and get you 2 stacks.
On the range minions you can do a W and right after it hits Q so the minions will get low from W and the Q will finish them off giving you 2 stacks.
Try to farm from a far to not get poked by the enemy mid laner veigar got the range to stay at a safe place and farm stacks at the same time.

I hope you enjoyed my guide anyone who read through all of it, I put a lot of time and effort into it and I would like if you can show some support to the guide.