Hi, i'm zuparoeban (don't ask me about my name xD) this is not my first build, but it is the first where i'm going to explain my choices. please don't mind the mistakes i have made (i probably will) and try to focus on the build itself and not on specific details, i do have to admit that my english isn't that good. have fun and i wish you luck! :)

I take marks of insight as they the only marks fit for a mage. for seals i take seals of replenishment, you want to have these as you need the mana regen at the start but at late game you'll have such a big mana pool that there will be no need for regeneration as it won't get empty before you get back to base. for glyphs i take glyphs of knowledge for the extra mana and no ability power glyphs because ryze doesn't really benefit from them. for quintessences i take spell vamp runes, i haven't tried this yet so i use mana per level quintessences for now, i will buy them when i have the money and edit this part if nessecery.

For masteries i take 9/0/21 getting two points in butcher and one in mental force as the ability power, as i said, won't do much for ryze and the aditional damage for auto-attacks helps with farming. the CDR and magic pen are very usefull as ryze is a mage. in the ultility tree i take mana per level, mana regen, spell vamp, increased xp gained, cdr, movement speed and cdr on summoner spells.

To start off you buy a saphire crystal for more damage on your q and w and a larger mana pool, you also take two health pots to keep you in lane.

on the first time you go back try to buy boots of speed and tear of the goddess so you are faster have more mana and mana regen and so you can get your tear of the goddess' passive up (4 bonus mana on each spell cast 1000 max bonus mana).

after this it's really up to you how you want to buy your stuff, need more mana regen? go for archangels staff, need more health? go for rod of ages, need more armor and/or cdr? go for glacial shroud, need more magic resist? go for negatron cloak. you core is: sorcerers shoes, tear of the goddess, glacial shroud (or frozen hearth),negatron cloak (or banshee's veil).

your final item is crucial, you take rabadons deathcap if you want to be full mage by getting so much ability power that it becomes a little bit usefull at last! or you take guardian angel to be a tanky mage and revive yourself after dying + more magic resist and armor.

Of course i max overload first as it is your main harrasment spell and it adds cooldown reduction. secondly i max rune prison as it's CC duration gets longer and damage gets higher. lastly i max spell flux because it doesn't benefit from your maximum mana. deperate power is maxed as soon as possible, at levels 6,11 and 16, because it's your ult which adds more mana and gives you spell vamp and 50% AoE damage for a few seconds when activated.

Feel free to farm a large group of creeps with your ultimate as its cooldown is very short, you can also try to farm with spell flux but that only works when there are minions with very low health.

I hope you liked my guide for ryze and enjoyed it, i also hope it helps you playing ryze and get good scores out of it!