Take Flash+ barrier, exhaust, or ignite if you are sure you can handle enemy mid laner. Do not take TP, if you wanna roam, just push a wave and go other lane. Your E gives you enough gank potential.

People do not get how powerful GLP on some mage champs is. High elo orianna main inspired me to inventing this build. Here is video about her: https://www.youtube.com/watch?v=XiELjcGsUF8. GLP is must be item for veigar: gives you some hp, mana and additional burst. You will not need your r at all to burst carries and midlaners thanks to this item !

Do not buy : Rod of ages - GLP gives you same passive, and additional burst.
: Morellomicon - Unless enemy has voli/vlad/mundo/swain/aatrox.
: Luden's Echo - You dont need that thing at all. Better take rabadon's deatchcap.
: Tear - Actually it is good item on veigar, but does not fit to this build at all.

Tanks are serious problem for many mages including veigar. This build fixes that. GLP + 3 penetration items and rabdon's cap can shredr almost whole health pool of any tank. Sometimes if you are ahead you can one shot even full tank champions with this build.

Early try to last hit minions with q or/and poke enemy with this ability. Landed q on enemy gives same ap as last hit minion. This makes it more worth to poke with q(best is when u take 1 minion kill and land q in the same time) and take remaining minions with autos or sometimes w.

DO NOT AFK-FARM WHOLE GAME LIKE TYPICAL NASUS OR VEIGAR!

After 10-15 minutes you can start roaming if you are ahead on lane or if enemy came back to base and u see potential gank on any side.

ALWAYS go to calls. Drake is worth more than 3 ap/100 gold.

Remember: any assist gives you additional 5 ap, and landed skill on enemy gives 1. This causes that you take more benefits from fighting and helping team than from afk farming. Remember that!

With this build you can expand generic veigar's EWQR combo to much stronger ones.

1: All in combo- After landing E(or when some1 stunned enemy) you use W, then GLP, Q and R at last.(E>W>GLP>Q>R)
2: GLP chase combo- After slowing enemy with GLP you land your W, Q and possibly even R on enemy.(GLP>W>Q>R)
3: fast combo - GLP, then Q and R instantly after GLP. Enough to kill targets missing some hp.(GLP>Q>R)