This is my first build guide (and hopefully no one has posted it yet), but the build is pretty destructive. The build has over 650 ability power, and a ridiculously high amount of magic penetration (85% I believe, including Xerath's Locus of Power). This allows you to almost literally rip someone apart with magic, while having some spell vamp to keep yourself alive, with max cooldown reduction without going over 40%.

Using this build will require you to play defensively at the beginning, since you don't have much ability power to poke hard with nor the ability power to get Xerath's armor passive up. Just don't feed the other team and you should do quite well with this build.

I recommend the following, but you can use whatever runes you're comfortable with:

Greater Marks of Knowledge for extra mana and more ability power from Archangel's Staff.
Greater Seals of Replenishment for higher mana regen at early game (since mana regen is not a major issue at end game).
Greater Glyphs of Force for higher ability power near end game.
Greater Quintessence of Avarice for extra gold over time and get your items faster without severely impacting anything.

Using the 9/0/21 masteries above will add extra cooldown reduction, some more ability power, extra mana regen, allow you to reach level 18 much faster, and add slightly extra gold throughout the game.

The masteries are pretty much self explanatory though.

Now here's the part you've probably been waiting for. Why did I pick those items?

Start off with a Meki Pendant, a health potion, and a mana potion; the meki pendant will add some mana regen to last longer before running out of mana, a health potion just in case you need to recover health, and a mana potion to get some mana back quicker than waiting for mana regen.

Grab a Tear of the Goddess, Boots of Speed if you can, and some more potions if you need to, the Tear will be to start gathering mana for your Archangel's.

Follow up the Tear with Boots of Lucidity to have your movement speed done and some more cooldown reduction to go with your masteries.

After the boots, go for your Archangel's Staff. You should have quite a bit of mana accumulated from the Tear and the conversion from mana to ability power will give you a nice jump in damage output, but it's not enough for us though.

The next part you can do in any order you wish.

Now go for a Void Staff, it provides some very good ability power and 40% magic penetration (add that with Locus of Power and you've already got a lot of magic penetration).

Since the Void Staff is done, you'll want to go for Morello's Evil Tome. The Tome adds more mana regen, the last of your cooldown reduction, and a lovely 75 ability power, making you even more dangerous to be close to, let alone within a tower and a third's distance (thanks to Locus of Power).

After Morello's, you're going to want to get at least a Hextech Revolver (if you can grab Will of the Ancients). The Revolver will give you 40 ability power, and 15% spell vamp (allowing you to finally heal yourself with your massive damage output).

Finally, grab Rabadon's Deathcap, it will give you the final chunk of ability power for your build.

If you didn't grab your Will of the Ancients before the Rabadon's Deathcap, grab it now since it grants you 80 ability power and 25% spell vamp, with 30 ability power and the 25% spell vamp also affecting your teammates.

Remember: The Void Staff, Morello's Evil Tome, Rabadon's Deathcap, and Will of the Ancients can be gotten in any order you choose.

The skill sequence starts off with your main source of damage output first, followed by your single target stun, and then your increased range with magic penetration. Continue from there to level up in the order of "Q, W, E, Q, W, E", breaking the pattern for your ultimate; just remember to continue from where you left off.

If you want, do your own level up pattern. Experiment and find the best sequence for you.

I picked Clarity and Ignite because those are my normal summoner spells, since I mostly play mages or support, but I'll list all of the spells and let you pick your own out of how well they are to you.

Exhaust: Slow your target and reduce the damage they can do. Great for preventing your target from running, making their damage insignificant on you while you burst them down, or great to make a pursuer not catch you.

Ghost: Run faster and ignore collisions. Great for running away or running into battle.

Heal: Heal yourself and nearby allies. Not exactly the greatest summoner spell, but it's useful if you expect to take a lot of damage throughout the game and don't want to waste potions or your healer's mana.

Teleport: Teleports you to an allied minion, turret, or placed object. Useful for getting back to your lane quickly or teleport behind enemy lines (if you have something to teleport to).

Revive: Bring yourself back from the dead quicker. I personally don't use it, because I don't expect to die very often to condone getting it, but I guess it's good to get back to a battle without having to wait.

Smite: Deal massive damage to a pet or creep. Great for a jungle build, but this isn't a jungle build.

Cleanse: Remove crowd controls from yourself, and reduce subsequent crowd controls by 65% for 3 seconds. I guess it's good, if you're going up again "crowd control city."

Fortify: Causes all allied turrets to take no damage and attack 100% faster for 6 seconds. Good for keeping all your towers defended if you're not at the tower(s) or need the defense/extra damage.

Clarity: Restore mana to yourself and nearby ally champions. I personally use this since it gives you more mana to use in early game; only downside is that it gets fairly useless near end game.

Ignite: Lights the target on fire, dealing true damage. I also use this spell since it allows you to get extra damage out on the target (very useful if they're running out of your range and Locus of Power is down).

Rally: Summons a beacon with health to increase allies attack damage for 15 seconds. This is kind of good, I think; it allows you to grant slightly more attack damage and could possibly cause the enemy team to attack the beacon instead of you or a teammate.

Clairvoyance: Allows your team to see a small part of the map for 6 seconds. This is good if you like to keep bushes checked for wild Garens (they're there even if you don't have Garen on either team), and all that cool jazz; I use clairvoyance for my support build, substituting Ignite.

Flash: Teleports you a short distance to the direction of your cursor. Great for getting away from a fight that's not in your favor, jumping over walls, or preventing an enemy's escape.

Which spells are for you?

The masteries are self explanatory, the spells are my personal pick (use whichever you want), the runes are what I recommend (use any runes you want), skill sequence lets you have consistent damage while leveling up, and the items give you massive damage, a lot of magic penetration, some spell vamp for some survivability, and max cooldown reduction.

Best of luck to you with this build, and may you control all the magic.

If you have any, I'd like some pointers to make my guide better.