This is my hybrid build for ryze. You get a lot of AD and AS from Manamune and malady, while still getting a heavy amount of mana to keep your abilities relevant. This will allow you to push towers more effectively and give you some continued DPS in addition to the pure burst damage from your spell combo

The runes are something that is completely up to your preference. I personally enjoy being able to deal a decent amount of damage while being able to take some myself; I chose MR and armor, scaling by level in yellows and blues, while taking armor penetration in reds and quints.

In the masteries tree I put 9 into the offensive tree for reduced cooldowns and increased magic penetration (my build provides no flat MPen otherwise). I put 7 into the defensive tree mainly to max out the Strength of Spirit skill, which is IMO a necessary skill on any ryze build. This is because ryze is designed to have upwards of 4000 mana, which will give you insane amounts of health regeneration that you would not be receiving otherwise. The rest of my mastery points are put into the utility tree, IMO this isn't the only place they could be placed, it all depends on preference.

The Best:
Ghost - This is a very versatile summoner spell in that it can help you get back to lane, set up a gank, escape from a gank, back door towers, chase enemy heroes, etc. It really is a great spell to have on almost any champion, and ryze is no exception.

Flash - Absolutely amazing summoner spell for most of the same reasons as ghost, except flashing over a wall is simply cooler and alot of times a more reliable escape mechanism than ghost. This spell also works well with your W spell, in that you can flash into range and quick snare them into place, ensuring you will get the rest of your spell combo off without much difficulty and probably get a few physical hits in as well.

Exhaust - Also a great choice in terms of summoner spells, especially when going against a physical carry such as Corki, Yi, or Tryndamere. I however, think that having the double escape is a better option, just because I really hate being ganked, but if you would prefer to take exhaust, then by all means take exhaust.

Teleport - while I really like this spell, and it can be very good for back dooring towers, which this build is decent at, I prefer the use ghost because it has many more uses IMO. The only exception to this rule is if your team has; A. a teemo or B. wards. If either of these are true, then teleport is a great spell, because you can teleport to a shroom or ward and set up some pretty amazing ganks with your team.

The Decent:

Cleanse - certainly a great spell to have in the other team is very CC heavy, but I rarely take it, and have a bad habit of forgetting to use it when I do take it.

Clairvoyance - a great spell to have on your team, and if you are a pro with it, then you were probably going to take it anyway, I just think that it would be better placed on a support champion

Fortify - a great spell to have on your team, and if you are a pro with it, then you were probably going to take it anyway, I just think that it would be better placed on a support or tank champion (yes I did just copy and paste the same description, its because I have the same opinion on both of them)

Clarity - while an early game ryze who is doing a lot of harrassing might wish they had picked this, it is not a viable spell on a champion who's mana reaches 4000+... end of story

Heal - If you often find yourself needing it, STOP BEING SO AGGRESSIVE!

Ignite - Ryze has enough damage output, get something more useful

The "WTF why would you use those?!":

Rally - BAD, BAD Nooby!

Revive - EVEN WORSE!

The items are where this build gets quite a bit different from more contemporary ryze builds. Instead of JUST stacking mana and AP, I chose to invest in some AD (through manamune) and AS (through malady). IMO this makes for a more balanced and unpredictable ryze. The passive on Malady is absolutely insane on ryze as you can rush into a fight, use your Q-E-W combo, get a few physical hits in, reducing their MR, then hit them again with the Q-E-W combo for even more damage. This build is also much better at pushing towers then the typical ryze build, because spells can't hurt towers. You may ask, "if you are going for an AD build, then why not get a Sheen/Tri Force/Lich's Bane?" IMO your Q-E-W combo should be executed extremely quickly, and stopping in between every spell to auto attack just ins't an effecient way to use that spell combo.

Pros:
-Great at pushing towers
-Very unpredictable damage (AD or AP)
-Abilities still hit pretty hard (build provides alot of mana)
-Solid amounts of Armor and Magic Resistance provide for tankiness
-Getting an Archangel's Staff at the end provides a good amount of AP as well

Cons:
-People will think you are weird
-Not AS MUCH mana as other ryze builds

Just so everyone knows, I built this more as a way to troll games, not as a competitive guide. Please don't run into a high ELO match toting this build and then come crying to me when you get your @ss handed to you, because the chances are that it WILL happen! I also didn't really test this build very much, so if you have any suggestions on alternate items/skill sequence/summoner spells/runes/masteries/guide font color just let me know! Once again, its a troll build, don't freak out and down vote it, my only real goal is to see an enemy player using this guide in-game.