Gather round, children, gather round-- there is much to discuss. Since his release, two things have been accepted about Kassadin:
1. He's a (mediocre and situational) burst mage assassin.
2. His W, Nether Blade, is barely useful for its passive and was certainly designed by accident by competent, professional developers (and should always be maxed last, because it's useless.)
Now, why do people believe these things? Because they're stupid, and I hate them. They cry in tongues and sacrifice lambs to the Metagame and when the Metagame says Kass is a mediocre and situational burst mage assassin, you malformed infants obey.
BUT THAT'S WRONG, IDIOT. STOP IT. TAKE A BATH.
Today, we are going to discuss Melee DPS Kassadin. Melee DPS Kassadin will put out a forest fire by bludgeoning it with a glowing sword. Melee DPS Kassadin will autoattack Lee Sin to death without expecting or receiving any consequences. Melee DPS Kassadin is your real father, and your real father's father.
HOW DOES IT WORK, DOC?
You get mostly defensive runes and Attack Speed marks, and go 20-10 in your masteries (if you don't get Spellsword on Kassadin, I swear to @Ezreal I will find you and euthanize you like a sick dog.) The idea is to get enough defense to not evaporate in teamfights, while stacking as much piss and vinegar into your on-hit melee damage as possible.
-You'll be defending yourself with Wit's End and Rod of Ages. If you're too awful to survive with just that (spoiler: you are, and I'm ashamed of you,) then grab another RoA or Frozen Heart. Something with lots of mana.
-You'll be doing damage with Berzerker's greaves, W (Nether Blade,) Wit's End, Muramana, Malady, RoA, and Rabadon. Before we wade into the insanity of your on-hit effects, remember that Muramana puts you around 195 AD before we add on all the good parts. Wit's End and Malady bring W's base damage up to 147, while Malady and Spellsword bring W's AP scaling up to 45%. RoA and Rabadon give you around 200 ap, which turns into around 90 bonus magic damage. Now activate W and add Muramana's toggle onto that, and you're doing more damage to your enemies than the gutter behind Wendy's is doing to your mother's knees.
But you still max W last, right? Because the Metagame says it's useless?
What did the doctors call your syndrome? It's not contagious, is it? Nether Blade is Kassadin's BEST ABILITY. Its passive means being OOM lasts roughly one second and its active effect lets you ramp up your melee damage FAST if you max it early (which you will do from this point forward.) It also gives you an extra on-hit effect which blends extremely well with on-hit items (as I explained above-- go read it again before your blank, reptilian brain forgets it, you awful mistake.) Maxing W first is also not something your idiot opponent is expecting, because your idiot opponent doesn't know how to play Kassadin correctly. After maxing W, max Q because Q is mind-blowingly awesome against literally everyone. I would say it's not as effective against auto-attack heavy carries, but you can out-DPS Master Yi so who cares.
What's the build order, sensei?
Boots and three pots -> Tear of the Goddess -> Wit's End (get the MR first, not recurve, you dunce) -> Berzerker's Greaves -> Manamune -> Rod of Ages -> Malady -> Rabadon's Deathcap.
Wait, why get Deathcap LAST on an AP champ?
Because Melee DPS Kassadin can win a game with the other five items anyway. If the game drags on long enough for you to buy Deathcap, your opponents will then see a sixth item in your inventory called "TAKE. THE. HINT."
Is there anything else I should know?
Not off the top of my head, but I'm sure you lepers will need more help. Feel free to ask any questions that your vacant skulls can string into a sentence, and I'll be happy to help.
Remember that playing Melee DPS Kassadin will earn you the esteem and envy of your peers, but will never extinguish my searing contempt for all of you. While I hate you all as a group, each of you is a unique snowflake with one-of-a-kind traits that make me hate you, specifically. Inquire, and I will be happy to elaborate.
TL;DR:
You're on a message board for a video game you take entirely too seriously. Your time is not valuable. Scroll back up there and read it the right way this time, you simpering parasite.