Hello, and Welcome to my "Hipster" Ryze build.
This Guide will teach you a bit about Ryze top. Its for all of you that want some easy answers, or a good build quickly. I made it for all off you that want to know a bit about the early game to and into late game build. Also, i recommend you to keep an open mind about things. Though I don't want you to play all the way after this guide. Its just some guidelines to help you into ownage.
PLEASE NOTE:
This is my first build guide, and please leave a comment about things i can do to improve it. And also, do up-vote it. I'll always try to respond to all feedback and constructive criticism.

Note: the early game items are highly optional, if you want to build something else, you can.
Example 1.:
An [Vampiric Scepter]] is a good option. I sometimes go for it, but you loose some on the spell dmg, but its worth it early. Switch it out with [Warden's Mail] if you feel like it, but i would still go with my personal build late - game.
Example 2.:
You could also think about The Brutaliser. Though this item is rather expensive, and should only be thougth of if you want to experience with a Black Cleaver. Its a great item, if you want to rely on BA damage, instead of spell damage. Though then the whole build is not as good, and you should change out more items.

EARLY GAME
When playing Ryze against an mele solo-top, you should think about playing aggresevly. If not, try to farm close to turret, as well as using spells, to get up stacks on the Manamune. This is to turn this into the Muramana. Make sure you always have some mana though, because this is vital as a caster. Make sure you always have more than 500 mana. And also, be sure that when you play against people with effect CC(silence, taunt) keep at range and make sure you're snare works out to use that range to the most.
MID GAME
Try to keep farming through mid game. This is needed to make sure you're gold stays up, if you're team aren't aggressive. If you are in a aggressive team with for example Jax; then try to force a fight mid-lane, and deal massive damage. This should only be done if you have enough farm to have some of the late game core items.
LATE GAME
Just kill everyone. Its a simple as that. If you have good team mates, and a full out build, I recommend you use all your OP epicness, to end the game violently and quickly.
That is, of course, unless you're carrying. if you are doing that(Something that you will, because solo queue is just hell) then try to give you're team mates the kills, and make sure you do everything you can to make you're teammates better. After All, its a teamgame.

RAINBOW
RAINBOW
RAINBOW
RAINBOW
RAINBOW
RAINBOW
At least i tried making a good guide. Have fun playing Ryze, and play you're game, to the max!