Don't forget. This build still in development and it will get update everytime when I get better idea.

UPDATE v1.0 RELEASE
Build added.

UPDATE v1.1
Builds updated

Veigar is a powerful burst mage known for his ability to stack AP (Ability Power) and scale into the late game. Here are the details of his abilities:

Baleful Strike (Q):

Veigar's Q is Baleful Strike. When cast, it targets an enemy unit, dealing magic damage. If Baleful Strike kills the target, Veigar gains a stack of Phenomenal Evil Power. These stacks permanently increase the ability power of his Baleful Strike, allowing Veigar to scale throughout the game.
Dark Matter (W):

Dark Matter is Veigar's W ability. When cast, it creates a gravitational field at the target location. After a delay, a burst of magical energy falls from the sky, dealing magic damage to all enemies in the area. Dark Matter is a significant source of burst damage in Veigar's kit.
Event Horizon (E):

Event Horizon is Veigar's E ability. He summons a cage at the target location, stunning enemies who pass through the edges after a delay. This ability provides crowd control and is crucial for setting up Veigar's combo or protecting himself from threats. A well-placed Event Horizon can turn the tide of team fights.
Primordial Burst (R):

Veigar's ultimate is Primordial Burst. When activated, he blasts the target enemy champion with dark energy, dealing magic damage. The damage is increased based on the target's missing health. Primordial Burst is a powerful finishing move, especially against low-health enemies.

How to Play Veigar:

Stacking AP:

Focus on last-hitting minions with Baleful Strike to gain stacks and increase your AP. Veigar's scaling is crucial for reaching high burst damage levels in the late game.
Poking in Lane:

Use Baleful Strike to poke your opponents in the laning phase. The ability has a relatively low cooldown, allowing you to harass enemies and gain AP stacks.
Combo Execution:

The standard combo for Veigar is to stun enemies with Event Horizon (E) and follow up with Baleful Strike (Q) and Dark Matter (W). This burst combo is potent, especially as you accumulate more AP.
Event Horizon Placement:

Mastering the placement of Event Horizon is key. Use it to zone enemies, catch opponents out of position, or set up ganks. It's a versatile tool that can be defensive or aggressive.
Farming and Waveclear:

Veigar's Dark Matter provides strong waveclear. Use it to farm minions efficiently and create pressure on the map.
Vision Control:

Vision is crucial for Veigar to avoid ganks and set up plays with Event Horizon. Place control wards and use your trinket wisely to ensure you have vision control in key areas.
Roaming and Team Fights:

As Veigar, roam to other lanes when you have pushed the wave or gained an advantage in your own lane. In team fights, focus on landing your stun and bursting down priority targets with your combo.
Build Synergies:

Build items that synergize with Veigar's burst damage, such as Luden's Tempest, Hextech Rocketbelt, and Rabadon's Deathcap. Adjust your build based on the enemy team composition.
Late Game Scaling:

Veigar is a late-game monster. As the game progresses, your AP will skyrocket, and your burst damage will become devastating. Position well in team fights, use Event Horizon effectively, and delete high-priority targets with your combo.
Objective Control:

Use your burst damage to secure objectives like Dragon, Baron, or turrets quickly. Your abilities make you a threat in securing objectives for your team.
Veigar excels at punishing opponents who underestimate his scaling and burst potential. Focus on farming well, securing kills, and stacking AP to become a late-game powerhouse. Properly executed combos and strategic use of Event Horizon can make you a formidable force on the Rift.

Laning Phase:
1. Farming and Stacking:

Prioritize last-hitting with Baleful Strike to accumulate AP stacks. Successfully managing your Q usage allows you to grow your power exponentially throughout the game.
2. Trading Patterns:

Utilize Baleful Strike to poke enemies, especially when they overstep or attempt to trade. The threat of Dark Matter and Event Horizon makes Veigar a potent laner if opponents underestimate his burst potential.
3. Wave Management:

Use Dark Matter to efficiently clear waves, creating pressure and allowing you to roam or secure objectives. Efficient wave management is crucial for controlling the pace of the game.
Mid and Late Game:
1. Burst Combos:

Mastering Veigar involves seamlessly chaining his abilities. Engage with Event Horizon to stun, follow up with Baleful Strike, and finish with Dark Matter. In team fights, prioritize squishy targets to maximize your impact.
2. Event Horizon Placement:

The correct placement of Event Horizon can be game-changing. Use it to peel for your team, cut off enemy escapes, or catch opponents out of position. Effective zoning with E creates opportunities for objectives or engages.
3. Roaming and Map Presence:

Roaming to other lanes, especially when your ultimate is available, can turn the tide of battles. Communicate with your team, roam strategically, and capitalize on the chaos caused by your burst damage.
4. Vision Control:

Proper vision is crucial for Veigar's safety and effectiveness. Ward key areas, especially when sieging or contesting objectives, to avoid surprise engagements.
5. Itemization:

Veigar benefits from items that enhance his burst potential and survivability. Consider core items like Luden's Tempest, Hextech Rocketbelt, and Rabadon's Deathcap. Adapt your build based on the enemy team's composition and threats.
General Tips:
1. Objective Securing:

Veigar's burst makes him valuable in securing objectives quickly. Use your combo to deal massive damage to Dragon, Baron Nashor, or turrets.
2. Late Game Scaling:

Embrace Veigar's late-game scaling. As your AP grows, your burst damage becomes astronomical. Position carefully in team fights, look for opportunities to capitalize on your scaling, and eliminate priority targets.
3. Defensive Play:

Veigar is susceptible to assassins and burst damage. Use Event Horizon defensively to disengage or peel for your team. Meditate on the potential threat and position wisely to maximize your survival.
4. Counter-Engaging:

Veigar excels at counter-engaging. When enemies dive into your team, use Event Horizon to stun and turn the tide. Your burst damage can quickly eliminate threats.
In summary, mastering Veigar requires a deep understanding of his scaling, precise ability usage, and strategic decision-making. By stacking AP, controlling the map, and executing well-timed combos, you can transform Veigar into a late-game powerhouse, decimating opponents with his dark magic.