Essentially this build is about pumping up Ryze's mana so that he can one-burst anyone down. Feel free to swap something out for a Void Staff if they're getting magic resist to counter you.

First you wanna start out with 4 saphire crystals, both for the cheap, easy mana bonus and because you're gonna make stuff from them. Once you have all 4, you need boots. Preferably finished, tier 2 boots. Then, start advancing all of your crystals to their second level; turn 2 of them into catalysts, one into a tear of the goddess and the last one into a glacial shroud, preferably in that order.

From there, upgrade them again, turning the catalysts into a Rod of Ages and a Banshees Veil, the Tear into an Archangel's, and the Shroud into a frozen heart. Again, preferably in that order.

Once you've completed all of those, and if the game hasn't ended yet, throw in a trinity force for a little more of everything.

With this build, I easily broke 5000 maximum mana, and my Q (Overload) was dealing an easy 600 damage per cast, with a 1.5 second cooldown. My snare (Rune Prison), was doing about 500 and Spell Flux about 300-400 per bounce.

A key component to this build is kiting. You are very squishy for quite a while, so stay safe. You will however, have a large damage output throughout the entire game, so don't be afraid to use it.