Kassadin is a burst, AP, mage that is a formidable opponent in both mid and other lanes. His harassing abilties (Q and E) make it exceptionally hard for people to farm, allowing Kassadin to gain an upper hand in early fights. This build will help you play a better Kassadin, but remember that this is just a HELP guide. You dont have to follow this to heart, so you can mix and match runes, masteries and abilities to make Kassadin to suit your playstyle. Remember, an annoying, fed Kassadin, is a f**king rape Kassadin. Enjoy!

For Runes I mainly focus on magic penetration and mana. With the combination of magic pen and a large pool of mana, Kassadin can harass very well, very early. Health quintessences will help your survivability, and extra movement speed is always a plus.

For Masteries, I go a 21 / 6 / 3 build.
With the damage output and extra AP from Ignite, from OFFENSE, the magic res and armour, and cooldown reduction on heal, and the death time reduction and HP/MP regen, Kassadin can successfully harass and survive in any lane. These masteries have good synergy with his Runes and Summoner Abilities.

Items are revolved around AP, mana, and health/armor/magic res (depending on opposing team, choose your defensive items wisely)
Getting Archangels and Mejais are a MUST in any build, and defensive items can vary depending on your enemies. Note that Kassadin's passive will help him survive in fights, so remember to take that into account when buying items.

Kassadin's skills have a nice combo to them, being able to dish out LARGE amounts of damage in the time frame of a few seconds. Using a basic R , E , Q combo will cut down lots of hp, and coupled with your items, masteries and runes, you'll be raping anyone in your path.
Also remember that your R is a SKILL SHOT! IT SHOULD BE TREATED AS ONE!!! Dont just willy nilly use it anyhow in any situation JUST to deal damage. It can be used to initiate as well as escape, making it the deadliest skill in your arsenal.

DO NOT UNDERESTIMATE HEAL!!!
Heal is a VERY good summoner spell. It has many luring capabilities and is an all round surviving tool. In team fights, as well as one on one skirmishes, heal can provide you with that edge to annihilate you enemy, and riftwalk out of harm. In mid, when on low hp, get into your opponents sight and use recall (B). When they move in for the attack, quickly use Heal and riftwalk into them, followed by your basic skill combo. This is an EXTREMELY effective way to dominate in mid.

As with ignite, its pretty obvious. Damage. AP. What more could you ask for?

Kassadin is the best melee mage out there (in my view). He has a silence, a slow and a teleport, basically making him the best, bursting ninja out there!
Have fun!