This guide pretty much optimized ability power while also making Kassadin less squish so you can deal more damage and live longer.

Pros:

Very high damage (Best DPS in game IMO)
Good Mobility
Good silencer
Very strong late game

Cons:

Very weak early game
Somewhat skill intensive

: Probably one of Kassadins most vital skills. Without this skill Rift Walk is left almost useless as an escape tool. When not on cd Kassadin is near invincible.
: Another not so much essential skill but very useful. Teleport can be used in a variety of ways with Kassadin whether its pushing lanes, defending or even ganking. This skill really helps Kassadin be all over the map at once.

The reason i have chosen to go with Defensive Masteries instead of Utility is because the Defensive mastery tree provides much more bonus's to Kassadin as a glass cannon. just take a look for yourself i wont be going into detail.

Core Items:

What you want to do to kill everyone is basically Rift Walk in, Null Sphere, Force Pulse. If their still not dead then continue chasing and Rift Walk again then another Force Pulse should do the trick. In the order Null Sphere and Force Pulse can be swapped around if you feel the need but personally i like having them silenced so they cant do anything to me and i generally leave unharmed.

Early Game (Solo):

What you want to do is basically start harassing with Null Sphere when its about level 3, Anything before and its just a waste of mana. I cant stress this enough but LAY BACK, Kassadin is incredibly squishy early game and must be treated so. In saying that if the opportunity comes go for the gank but always be aware. As soon as you have 925 gold head back for Catalyst Of The Protector, This item is essential to get as soon as you can because it allows you to stay in the lane longer and harass more.

Early Game (Sidelane):

This is basically the same as solo but you have to be extra careful because you wont have the advantage of being a high level and you have to watch out for two enemies.

Mid Game:

Now things start picking up. Try to get Mejai's Soulstealer as soon as possible and start getting stacks on it. If you're soloing mid Teleport to another lane and gank someone. Remember to always go to the lane where the enemy has pushes farthest. When you start getting higher level you can start being more aggressive because of the more health and damage but don't do anything ridiculous. If you get in trouble Cleanse then Rift Walk out. One tip i cant stress enough is to play as if Cleanse is on cooldown.

Late Game:

Now the fun begins. By this time you should be working on if not completed Archangel's Staff. Be on the lookout for squishy's to feed off of. During this period you are probably one of highest dpsers in the match.

Team Battles:

As Kassadin you play a different role in Team Battles. What you have to do is not attack the tank or who is supposed to be focused but to attack the squishy's a.k.a. the casters and dpsers killing your team. Once this is completed your team will have killed the tank if not you can finish him off and you have won the battle. Some things to kee pin mind Don't use melee, Stay on the outside of the battle, If your being focused Rift Walk out.

Thanks for reading the guide if you think there is something wrong with it please comment!

xSilas43

Credits:

To killraven who's guide got me into playing Kassadin check out his awesome guide here.
To Searz who's guide changed my opinions on the mastery tree.