I play the kassadin role extremly offensive AP.
This is a guide to a Kassadin that deals high AP damage and 1 on 1 he is very hard to break down.
I focus only on the AP, but also a little on cooldown reduction and on magic resist.
Kassadin is used almost only for the mid-lane. He is extremly good at picking single target after he got his ULTI.
That is also why I play him, because he is so good at dealing quick damage and getting out of combat very fast. His abilities can be used as offensive, but also as defensive. He is hard to kill and deals a lot of damage.

For the runes I try to make up for the defence that I dont have.
That means that I will focus on health and armor, but also mana, because of Kassadins high mana use.
Health seal for some early laning control, so that it is as easy to get killed, so that you can hold the mid-lane longer.
I also have Mana Quints, so that I dont use a lot of mana, because even if he has his W, if u spam his ULTI in a chase, then it can cost a lot of mana.
Others would take the AP runes, but the reason a take these runes are, that I have trouble with gettig health, and especially at the early game, but I also have the trouble at the late game, because I can only take down single targets, before the rest of the team jumps me. That is the reason I take these defensive runes.

For the masteries I take 22/0/8, for some good offensive runes at the 22.
I focus much on the damage that can be dealt out, so that a good early game with the Q.
I also take the Utility masteries for the manaregen and the mana pr. lvl.
These masteries work good for me, and increases the damage, that Kassadin can deal thoughout the game.

Items I take no prisoners.
Rod of Ages: For the AP, health and mana.
Sorcerer's Shoes: You got to have at least some kind of shoes and the sorcerer's have the extra from it's 15 Magic-penetration.
Rabadon's Deathcap: The must powerful AP item in the game. It gives 120 AP and 30% extra in AP. It is an item that you have to got, no matter who you are playing against. You can't get an AP item that is more powerful.
Void Staff: The Void Staff is an awesome late-game item, that can help a Kassadin deal high damage to low health champions. It has 70 AP and 35% Magic-Penetration. A great offence item, like the rest of the build.
Athene's Unholy Grail: It is my answer to the defensive build, it gives some Magic Armor, but also have a lot of other abilities, that are helpful to Kassadin, who has a big mana use.
Lich Bane: It gives 80 AP and the power of the Shen. Extra damage on your next basic attack after you have used an ability. It is great for an instant combat and can deal a lot of damage to single targets.

You should level up Q first, because of the damage that can be dealt out.
Next I would consider the W at lvl 2, because of the mana regen, but i would also like to max it as the last one.
I would take the E in lvl 4 and max it 2nd. It deals both damage and slow the target. An great ability for chasing others, and to let you escape to.
I take Ulti as you should. In 6 ,11 ,16.
It take Ignite for extra damage and flash for a fast chase or escape.

Creeping is hard, if you play against an agreesive mid-laner. He only have melee attacks, but he also has his Q to farm with. The only jungling you should do is in mid- and late-game, when there are no minions close to you. But you should also take a blue-buff if you can.

You should always try to gank in other lanes, when you have got your Ulti. It is great for ganking, because you can come out of nowhere and easyli damage and kill, without taking damage yourself. You can also assist the other team members with your Q and E.
In teamfight you should use your Ulti to get close and take down the Adc and squice targets on the other teams, but you should never start a teeamfight by jumping first in, because you don't have a lot of health.