Ok, please bear with me any only offer constructive criticism as this is my first build attempt on here showing a mage that shows promise of devistation. After watchign Ryze builds off the bots and other players I have come to realize that Ryze offers a chance for MAYHEM.

Here's the runes I chose and why. (keep in mind the runes are based on having all rune slots open)

Mark of Insight: You're looking at a 0.95/rune Magic Penetration..Ryze is a mage...thats a bonus of 8.55 Mag Pen to help bury that proverbial nail into the coffin. All Ryze dishes out is Magic Damage..you WANT THIS!

Seal of Vitality: Health...you're a mage..yeah, you need this too. To start off this isn't gonna seem like much, I mean a measely 1.08 Health/rune at lvl 1. Thats only a bonus of 9.72hp at first lvl. Now as you gain levels it gets a lot better. When you cap at 18, you now have a delightlful 174.96 hp bonus from all your runes. If you're wondering why I didn't chose an armor Seal instead, with the damge you'll be putting out, don't worry about it so much.

Glyph of Knowledge: He're is your bread and butter. It doesn't get any better than this. 1.42 Mana/lvl. 230 Bonus Mana at lvl 18, as opposed to the 101.25 that you'd receive from Glyph of Intellect. Ryze's abilities thrive on his mana points, the more max mana he has, the more damage he does..nuff' said.

Alright, I'm gonna do this as a short but sweet for each selection I've made.

Mental Force: Gives you a little bonus damage every time you pop off a skill..more damage = more kills.
Sorcery: Quicker CD's = Faster popping of them to dish out more damage.
Arcane Knowledge: 10% is 10% Penetration..especially when the Magic Mule is behind that face stomping you with a huge Magic Bonus Damage.

Good Hands: Its only a short bonus to time spent dead, but it means you're faster to get back in the fight.
Expanded Mind: More Mana...oh look, more damage. Nuff' said.
Swiftness: Gives you the bonus to catch up with the cowards fleeing for more kills or bail out in a fight if its starting to look like a prison shower scene.
Greed: More Gold = Buying your items faster = You kill more
Transmutation: Oh look, I'm doing magic damage and healing my life...this is an awesome bonus, even if only marginally.
Wealth: More gold to buy your goddies to start..EVERY TIME!!!
Intelligence: CDR..again, faster you can pop those skills off the more kills you'll be racking up and more gold too.
Mastermind: Because that's what Ryze is. A Mastermind of painful destruction who'd CDR is now maximizing and pimp slapping other Summoners where it hurts most...on the kill board.

Now for your items. I hopped over to http://na.leagueoflegends.com/items and spent a few hours reading through every items and based on theory to begin. Then I got in game and tried it out...holy jimminie cricket batman! It works very well.

Sorcerer's shoes: Since you'll be pumping out a huge amount of magic damage, these are idealistic to grind in that damage with the 20% bonus Magic Penetration. Beauty if, you already have a bonus to boot with it from your skills too, so now you have a 30% bonus within the first few minutes of the match.

Archangel's Staff: You definately wanna grab this bad boy next. EVERYTIME you use an ability, your mana increases by 4 (up to 1000 bonus). This alone is useful as your mana will constantly improve your damage as that increases parallel to mana increase. Not only that, but the passive grants you a bonus of 3% of max mana..oh goodie..more damage.

Frozen Heart: I chose this as the next item just to give a bit more survivability because you should now be at mid game point. 99 Armor bonus is really gonna help you alot here, especially when you just gained an additional 525 mana to help increase that % base to your damage. Final benifit off this item is where it gets the frosting of the cake. You just slowed you your enemies attack speed by 20%. So while they are slowly trying to beat on you, you're hammerfisting them with all that beautiful magic damage you're banking up.

Rod Of Ages: 450 health...um thank you? Now you're not gonna worry about dying as quick (unless you don't know how to run back and you just wanna stay up from and take damage...if thats the case..go pick a tank toon, not a mage). 525 Mana. I'll say it again...more damage. 60 Ability Power....oh look MORE DAMAGE!! MUAHAHAHAHAHA...sorry. Here comes the sweet part..ready? You sure? 18 Health, 20 Mana, 2 Ability Power EVERY minute stcking up to 10x. Thats a bonus of 180 Health, 200 Mana, 20 Ability Power. Talk about sweetness.

Odyn's Veil: This was my next selection. Sure, you get 350 health and 350 Mana for more survivability and increase on that cannon you're already firing, but here's the nice part; you just scored a 50 MR and it reduces the large damage opponents are putting out by 10%. The PASSIVE stores this damage up to a max of 200 damage and turns around and the ACTIVE on it releases 200+stored (max 400) damage. Can you say BOOM HEAD SHOT!! I knew you could.

Glacial Shroud: We finalize our great mage with this item. 425 Mana for some extra damage, 45 Armor for extra survivability (because we're now lvl 18) and a little topper of 15% CDR. yes the CDR's may seem a bit excessive at this point but when you're spanking the opponents and popping off skills as fast as Akali or Tryndamere does basic attacks, you'll be more happy with all those kills.

Exhaust: Opponents movement speed is reduced, attack damage dealt..reduced, ability and item damage...reduced. This is perfect for Ryze to have in his arsenal as you're gonna be cranking out huge damage getting your OVERLOAD off 1st then followed up by RUNE PRISON, which by the time that wears off, should be able to finish with another RUNE PRISON if needed. This combo is all about SLOW them down and hitting harder.

Teleport: I chose this because you never know when an ally will need help. Being a HUGE damage dealer you can pop in and provide some serious cover fire.

PROS
Heavy Damage output end game
You have Spell Vamp and all you do is cast mana, great for self healing
Quick CDR's with build listed
2 skills give you AoE's
2 single skills work based off max mana % for bonus damage...this build gives you the powder keg

CONS
You're gonna be squishy to start...harass opposing champions but focus on minions
Not as many AoE's as some other casters
team might call you a KSer for 1-2 hitting a Champion they were attacking...but thats the price you pay for Ryze Mayhem

Ryze is not for everyone! He requires a different style of playing that what I've seen most are used to. You have to know when to pick your battle to begin, how hard to push and be willing to hear others complain that you are OPed.

With that being said, its a game. Be willing to shrug it off, enjoy the game and stomp tthe **** out of opposing Champions with the high damge you'll be doing.

If anyone has thought my wording was a bit excentric, its because I enjoy adding a unique sense of humor to life..I'm sarcastic and thats the way it is. Feel free to use this build or not, choice is ultimately yours, but I welcome any constructive criticism on the build itself, not my choice of wording....keep up the good fight precious!