Starting with Kage's Lucky Pick jump starts your build and is an ingredient in a later item, making it practical for the start. Next get Ionian Boots of Lucidity bringing cooldown to 25%. now you want your AP, which comes from Rabadon's Death Cap. This is where you start getting ganked, so build your health(with slowing effect on the side) using Rylai's Crystal Scepter. Time for an extra attack, you want a Deathfire Grasp maxing your cooldown reduction at 40%(the max the game will allow) with its' nice true damage active(don't forget to hotkey it!). Again we're getting another attack, this one super powerful with your now high AP; shoot for a Lich Bane. By now everyone should be scared of you and will have built some magic resistance, counter it with your final item; a Void Staff.

Greater Marks of Insight provide magic penetration for the default 30 magic resistance everyone gets, bringing it down by roughly 7. Greater Glyphs of force give a nice kick in the beginning but a more useful wallop that's required late game for the tanks then massed health. While Greater Seals of Avarice and Greater Quintessences of Avarice may seem like something only a tank would use, they are very good for hurrying your build where all of the ability power comes from. On a side note, Brand isn't a squishy character. He's not a tank either but he has the possibility to build like one if need be and early game success can cause you to be the enemies first target priority.

Utility provides ok cooldown reduction, mana regen for early game when it's required, 15% cooldown reduction on heal and ignite, and 2 extra gold gain for-again-getting that build out as soon as possible. 9 in Offense brings cooldown reduction up to 10% with an extra 10% magic penetration and 4 AP on the side.

Pillar of Flame is Brand's most powerful ability, and most ranged, so get it at every opportunity. The game won't allow you to get the same ability twice in a row, so you have to stagger abilities. First you need one point of Sear for its' stun effect with Blaze. After that you max Conflagration whenever you can't get Pillar of Flame. You finish maxing Sear last. Pyroclasm, like all ultimates, must be taken at levels 6, 11, and 16.

Heal may seem like a nooby spell to use but is very essential to survival when getting ganked. Ignite has many uses: nullifying heals, catching runners, or just for extra damage.

By now you have 7 ways to deal extreme damage to opponents. You've got your 4 abilities, the Ignite summoner spell, Lich Bane's passive, and Deathfire Grasp's active. All of this makes Brand on the overall a total nuke, beware opponents! Just remember to utilize all that power! Get Tenacity if you're getting silenced too often to unload all your power!( Mercury's Treads)

I would like to explain the order in which to use your spells for maximum damage and efficiency and for the useful Blaze bonus that adds to your spells.

1v1:
Conflagration to start your Blaze bonus, Sear to stun them, Pillar of Flame to utilize that stun, a basic attack to get your Lich Bane passive damage, then Deathfire Grasp, Ignite, and Pyroclasm are free to pick up the kill if need be.

Team Fight:
Unlike a 1v1, start by using Pyroclasm. Then use Conflagration to get its area effect from Blaze. Now nuke the crowd with Pillar of Flame, they should all be a Blaze and take extra damage from this. Now you can target individuals with Sear, Ignite, Deathfire Grasp, and Lich Bane.

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Builds
1.If you are getting fed up with the constant ganks, Mercury's Treads are a choice instead of Ionian Boots of Lucidity.
2.If you are tired of having a mana problem early game, you could switch from Kage's Lucky Pick to starting off with building Mercury's Treads first, then shooting for a Fiendish Codex, and immediately afterwards, a Morello's Evil Tome, but then Deathfire Grasp wouldn't be required so replace it with a Will of the Ancients.
3.I realize Deathfire Grasp and Lich Bane are odd choices, I only use them for the two extra high damage attacks. If you'd like you have the choice to replace them with Mejai's Soulstealer, Abyssal Mask, Zhonya's Hourglass, or Odyn's Veil.

Masteries
1.If you don't like getting Greed , you can take just two points in Swiftness then take Transmutation , Runic Affinity , and Awareness .Offense Take Mental Force , Sorcery, Arcane Knowledge , Havoc , Blast , Archmage , and Executioner . Then in Utility take Expanded Mind , Improved Recall , 2 points in Swiftness , and Meditation .Greater Seals of Avarice with Greater Seals of Warding for protection early game against the other mage in the middle, or Greater Seals of Replenishment to help solve that early-game mana problem!
2.For the same reason you can replace Greater Quintessences of Avarice with Greater Quintessences of Potency for more firepower!

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jhoijhoi's "Making a guide" taught me to code, and every millimeter of it you see in here is credited to her! I literally had her coding instruction open on another tab the whole time I was making this guide! Thanks again!