Great Mid and solo laner
Very intimidating early game
Great Nuker
Once you have Rylai's, your utility becomes greatly increased

Very squishy early game and late game
Has almost no escape methods other than a single target stun
Pyroclasm is virtually USELESS unless there are multiple enemy champions or other targets

Greater Marks of Insight
Greater Seals of Replenishment
Greater Glyphs of Focus
Greater Quintessence of Ability Power

Sear --> Conflagration on the same target --> Pillar of Flame --> Pyroclasm

Doran's Ring --> Boots --> Needlessly Large Wand or Giant's Belt --> Rabadon's Deathcap Rylai's Crystal Sceptor --> Sorcerer's Shoes --> Will of the Ancients --> Void Staff --> Zhonya's Hourglass

Doran's Ring: I like to start off with a Doran's Ring. It gives you HP, AP, and mana regen, which is essential on Brand. With the mana regen, along with clarity, you shouldn't have to leave lane for the first 20 items. The only time you should go back is when you're low on HP, which should never happen thanks to his amazing ranged harass, or if you can afford any major items.

Rabadon's Deathcap: Rabadon's is great for Brand. The quick AP boost works wonders, but only start rushing this item if, and i emphasize, IF you can get it within 5 or 10 minutes. If you have 2 or 3 kills by the time you go back your first time or have more than 1600 gp for a Needlessly Large Wand, then definitely start rushing Rabadon's

Rylai's Crystal Sceptor: I usually rush Rylai's first by getting a Giant's Belt. This gives you a ridiculous amount of health early on for an AP Carry. The only issue is that you won't be doing as much damage, but honestly, as Brand, you don't NEED a lot of AP early game. Your poking and harassing should keep people back away from you, which sets up for easy ganks and dives in your lane. Now Rylai's gives you both a slow and 700 HP. The slow will help you land your stun, and let you chase better, even without tier 2 boots. The 700 HP boost also gives you more sustain, allowing you to really take some hits and not be afraid of going in for the kills. Rylai's, i feel, is essential for Brand since it gives him more utility in team fights and helps him sustain his lane better. The slow has also saved me countless times while running away from ganks.

Sorcerer's Shoes: Getting Boots is a must while rushing or between acquiring Rabadon's Deathcap and Rylai's Crystal Sceptor. You need some kind of boots by 15 minutes in, even if you are rushing another item. I chose Sorcerer's Shoes because they give you some magic pen, which makes Brand even more deadly than before.

Will of the Ancients: One of the best, but very under used, items in the game for AP carries. People don't realize how much spell vamp does for AP Carries, especially when you have a Rabadon's Deathcap already. The spell vamp, along with the HP from Rylai's Crystal Sceptor make Brand much tankier and have much better sustain in team fights. He can continuously stay in team fights while taking damage because his spell vamp will keep his health relatively high. Of course if you get focused down, nothing will save you, but you just have to be cautious in team fights.

Void Staff: This item gives you both AP and 40% Magic Pen, which lets you SHRED through tanks or anyone that has MR. Without void staff, the damage you do could be cut down in half due to Force of Nature and Banshee's Veil. It is essential late game if you see more than 2 characters with either of the two aforementioned items.

Zhonya's Hourglass: Okay, so the hourglass only gives you 100 AP and 70 armor. What's the use of that? More AP is ALWAYS good on Brand, and the extra armor is quite amazing. The last patch also made Zhonya's Hourglass 200 gold cheaper, which makes it easier to get, but the active ability is truly amazing. If you ever are in a team fight as Brand, you will begin to get focused down HARD. He is too much of a threat to be ignored, so when you do begin to get focused, you just activate Zhonya's Hourglass and become untargetable and invulnerable for 2 seconds. This is HUGE. Although you can't cast any spells while the hourglass is active, it allows you to avoid dying instantly, and possibly pull survive the team fight. As soon as the 2 seconds are up though, you have to either throw down ALL of your spells or run away and then throw down your combo.

--OPTIONAL ITEMS--

Banshee's Veil: Not needed for Brand, but it comes in handy when facing a team FULL of cc or against another huge AP carry doing well on the other team

Archangel's Staff: Takes too long to build up the AP, but if you really want to do it, Archangel's does give more AP than Rabadon's Deathcap. You get a huge mana pool by the end of the game, which means that you don't need clartiy, so I would grab either exhaust or flash instead.

Morello's Evil Tome: Great Item, but it doesn't offer as much as the items in the core build do. It gives AP, CDR (which is ALWAYS good), and mana regen, but the mana regen is wasted if you have clarity and mp5 seals. Again, if you do grab this, then you do not need clarity.

STILL UNDER CONSTRUCTION