Hi, this is my veigar build. I tried this a lot and it turned out very effective. I just wanted to make a quick guide. You can leave feedback.

Just usual Ap Carry stuff. You can replace Magic penetration runes with ap runes, but i suggest you to keep the defensive runes. It helps your early game survivability.

Keep the offensive tree. But you can get 9 points in utility tree instead of defensive tree if you believe your positioning is great.

Take 3 points of Expanded Mind
Take 1 points of Summoner's Insight
Take 3 points of Meditation
Take 1 points of Swiftness or Improved Recall
Take 1 points of Runic Affinity

First of all, dont expect to buy the same items in all games, they are just for the case where everything goes good. If you got trouble in lane dont worry to get one Doran's Ring or two. Play defensive and farm your Baleful Strike. You can get 1 or 2 last hits with your Baleful Strike at one wave. Dont forget to kill other minions with normal attacks. Dont use your Dark Matter to kill minions or harass, it would harm your mana at early game and push the lane.

If enemy jungler comes to gank just use your Event Horizon and fall back. If your jungler comes to gank, use your Event Horizon then use everything you have if you believe you can burst them down.

If no one comes to help, it's still okay. You can burst enemy mid solo easy. Just calcualte how much mana you need to pull of a full combo. If you have less, wait for it to regen. If you have more, harass them with your Baleful Strike before initation. After they lost some hp and you have enough mana. Initiate with Event Horizon and immediately cast your Dark Matter and Baleful Strike and Primordial Burst and Ignite in exact order. Congratulations on your first blood.

After you got Deathfire Grasp, do the same combo except that use Deathfire Grasp after casting Dark Matter but before it landing. This is to get maximum damage with Deathfire Grasp.

In late game team fights, dont inititate yourself. Just sit back and wait for teamfight to start. After it started, you need to choose your focus carefully. If they have a fed ap carry. Dont think, 1 hit them to death. If you get focused, Flash out of there and stun. After you 1 hitted your target. Dont overextend yourself, just wait at back for your cooldowns. Cast them when they are available again and be safe.

If your junlger is not mana dependent, take first blue. If he is, forget the first blue and ask for him to second blue. He will probably give it. You really need it for most needed mana regen and cooldown reduction.

If you have trouble with mana management, you can take Clarity instead of Ignite. But it will hurt your burst. Always keep the Flash it's a great escape mechanism.