Hello this is Bolter778 and this is my build to Mid Lane Ryze. Ryze is a very good champion that can spam abilities and deal a lot of damage. He is a good counter to summoners who play Fizz as Fizz can be very annoying with his Playful / Trickster.

Pros

-Very powerful late game (Considered an AP Hyper Carry)
-High damage/Burst damage
-Sort of tanky thanks to Rod of Ages, Frozen Heart, and Mikael's Blessing
-Low cool down thanks to Overload, Frozen Heart, and Intelligence
-Snare Spell Rune Prison
-Low cooldown and AOE damage ult with no cost Desparate Power

Cons

-Low ranged spells
-Easy to be Ganked if you aren't playing defensively
-Kind of weak early game

The item order for Ryze is basic. The standard early game Crystalline Flask, Sight Ward and Health Potion. I recommend going with 2 Faerie Charm and 3 Health Potion
After your first recall, buy the Tear of the Goddess because as Ryze, you spam your skills and Boots if you can.
Later on, you want to get Chalice of Harmony for Mana Regeneration and also to later build into a Mikael's Blessing and the catalyst the protector to have more survivabilty and Mana.
Transitioning to early mid game, get the Sorcerer's Shoes for Movement Speed and Magic Penetration and Glacial Shroud for Armor and Mana, also to build it into the Frozen Heart. Other viable boots depending on the situation are Mercury's Treads, for high ap and cc enemies such as Ahri, or Ninja Tabi, for high ad enemies such as Jax, Darius, etc.
The Archangel's Staff is standard for mages like Ryze and the Rod of Ages gives you Ability Power, Mana, and and more Health. (if you dont have inventory space sell the Faerie Charm)
Now as you go into late game, you want to finish your Frozen Heart, and Mikael's Blessing.
The Frozen Heart is for Armor, CoolDown Reduction, and Mana, while the Mikael's Blessing is for Magic resistance, Mana, and Mana Regeneration.
Finally, Finish off your build with a Void Staff and an Enchantment: Alacrity

Runes

For the Seals and Glyphs, get the standard Greater Seal of Armor and the Greater Glyph of Magic Resist since that makes you less squishy.
For Mark, get the Greater Mark of Magic Penetration obviously for the Magic Penetration.
Lastly for Quintessence, get the Greater Quintessence of Ability Power for the Extra Ability Power
Greater Seal of Armor
Greater Glyph of Magic Resist

Greater Mark of Magic Penetration

Greater Quintessence of Ability power

For masteries, take 9/0/21
9 in offense for standard mage attack points and 21 in utility for Movement speed, Cooldown Reduction, Lifesteal, Spellvamp, Mana Rengeneration, etc

When Ryze casts a spell, all other spells have their cooldown reduced by 1 second.


Passive: Ryze gains cooldown reduction.
Active: Ryze throws a charge of pure energy at an enemy unit, dealing magic damage.
Cost: 60 mana
Cooldown: 3.5 seconds
Range: 650
Projectile speed: 1400

Cooldown Reduction: 2/4/6/8/10 %
Magic Damage: 60/85/110/135/160/(+0.4 per ability power)/ (+6.5% of max mana)


Active: Ryze snares an enemy unit, preventing movement and dealing magic damage.
Cooldown: 14 seconds
Range: 625

Cost: 80/90/100/110/120 mana
Duration: 0.75/1/1.25/1.5/1.75 seconds
Magic Damage: 60/95/130/165/200/(+0.6 per ability power)/ (+4.5% of max mana)


Active: Ryze unleashes a bouncing orb of magical power which bounces to enemy units or himself, up to 5 times (for total of 6 hits). Each bounce deals magic damage and reduces the targets magic resistance for 5 seconds. If the orb bounces to Ryze himself, it will not decrease his magic resistance or deal damage.
Cooldown: 14 seconds
Range: 675
Bounce Radius: 400

Cost: 80/90/100/110/120 mana
Magic Damage: 50/70/90/110/130/(+0.35 per ability power)/ (+1% of max mana)
Magic Resist Reduction: 12/15/18/21/24


Active: Ryze becomes supercharged, gaining spell vamp, movement speed and causing his spells to deal 50% AoE damage.

Cooldown: 70/60/50 seconds
Spell Vamp: 15/20/25 %
Movement Speed: 35/45/55
Duration: 5/6/7 seconds

Overload (Q): I take this skill at level 1, 3, 5, 7, and 9. This is Ryze's main damage spell therefore you max it first.

Rune Prison (W): I take this skill at level 2, 8, 10, 12, and 13. This is Ryze's utility spell to escape by trapping or stop them from running away by trapping. This is a good combo with your Overload, Spell Flux, and Desperate Power. (Use Rune Prison first to trap, then use Desperate Power right away and Spell Flux for the Magic Resistance Reduction and finally Overload as a combo. Also put ignite in the combo)

Spell Flux (E): I take this skill at level 4, 14, 15, 17, and 18. This spell is mainly used in team fights or on minions to get cs. Spell Flux is especially good with Desperate Power because it bounces up to 5 times and does splash damage with Desperate Power.

Desperate Power (R): I take this skill at level 6, 11, and 16 like usual ultimates. This spell is very good since it has no cost and very low cool down. This is Ryze's steroid since it gives him spell vamp, movement speed and AOE damage. This is very good in duels, teamfights and clearing out minion waves

Good escape or chase when used with Rune Prison

Standard kill secure/heal block

Other Viable Options

Good for running away or chasing. This can be a replacement for Flash if you like Ghost over Flash

Great in duels or team fights(use on the champion that has the highest damage output). Use this if Rune Prison is not enough for you.