First build posted and all downvote :| thx for encouragement

forgot to downvote, reasons above.

sory about the spam, deleted the additional comments :)

the build is not about Athene's Unholy Grail, it is about the early chalice. it gives you a huge lane advantage and allows you literally to spam as much as you want so that your tear gets fully stacked faster. you can sell the chalice as well when you have enough gold to buy an extra item.

for zhonya's: you are quite tanky with ryze, but the actve can be useful if you get caught. ryze can survive one, maybe two champions attacking him without a problem, but when he is 5v1, he is just instakilled. also, you need the armor with this build.
i don't say it is one of the best items for ryze, because it is situational.

dude, your guide is the most incomplete one i have ever seen.
also, your item build works, but it is unconventional, so you need to explain it. also tear > chalice and you need to get roa at 20 or earlier, which is almost impossible with your build.

This little build is based on dmg not on survive.I will make a build too whit more survivable ryze and less dmg :) i think its ok.... i use this build and i alaways do a min of 15 kills in a ranked or normal game ! And yeah Athene unholy grail give magic resistance which is good!And Zhonya's is just for ability and armor!Try it out first of all!At start if you use correctly your skills at min 2 or 3 you do first blood than in late game u become OP :) just try it out!

Why...? Why Athene's Unholy Grail and Zhonya's Hourglass on Ryze? If you build him right you don't need such stats- you'll have enough mana to never ever need Mana Font, and if you build Ryze right he should be tanky enough to survive most teamfights without that active provided by Zhonya's Hourglass.

But make contents too!

Really nice build!