Kass's average day includes him completly owning everyone on the battlefield. one of my friends even got 27 and 4 with him. (not with this build but an alternate one farther down the page.) this build shows how Kassadin might even be more OP than Darius was when he first came out.
this does two things because both of your summoner spells apply to it.
exhaust - the enemy you use it on becomes weaker to your spells and attacks because of the mastery *hint hint* this is an extremely good time to use your nether blade spell and start your ignite on them (especially early game)*hint over*.
ignite - if you activate this while they're exhausted not only will they still be weakened from the exhaust but once you use ignite your spells and attacks become stronger while its on cooldown. this means that while they are weak you are strong take advantage of that.
basic ability power, completely nessecary.
cooldown reduction, this not only helps you with a certain idea mentioned in summoners spells but allows you to get arcane knowledge which is very helpful with the build.
this gives you needed magic pen., because of the lack of sorcerer's shoes, the only other magic pen. that you have is the 8.55 you get from the mark runes.
this just helps you with basic damage in general, it isn't necessarily needed, if you think there is a better mastery to replace it, be my guest it just should be in the offense category.
gets you more AP every time you level up, helpful because again the only other time you get the same thing is from your runes.
now the next mastery, (archmage,) gives you a higher percentage of AP, so this is helpful in general with almost everthing kass does.
the last mastery is exicutioner which gives you that bang you need when your level two and want to kill them. this is true because when your right next to them in the beginning and null sphere is on cooldown you activate nether blade and hit them once and exicutioner activates making you do almost a bar of health each hit with nether blade. then when they run out of your auto-attack range exhaust them and hit them more. use null sphere if you have it. then if that doesn't work ignite them. that is an early game kill that is helpful for money you need.
not much to explain here, mana is helpful, speed even more so, and runic affinity to make blue last longer for CD's and mana regen and thats it.
Now first I want to show you the build I mentioned earlier in the intro. It goes like thisOR or ( which ever you need more of Magic resist or armor) then or (which ever one you didn't get) Now to put it in words, boots of speed, 3 health potion, tear of the goddess, sorcerer's shoes, or the ionian boots of lucidity, Rabadon's deathcap, archangels staff, zhoyna's hourglass, or lich bane, then the other one of zhonya's hourglass or lich bane that you didn't get the first time, then 3 elixirs of brilliance.
these are the accepted summoner spells
slows them down and reduces their stats for a short time helpful for running away from 1v1 or stopping the enemy from running from a 1v1.
ignite is the one completly nessecary skill out of all of these just so you make sure to kill them even if you die/ they run away
flash is helpful because it can get you out of some situations but so can your ult which is why this build has cooldown reduction so you can riftwalk in, kill them, and riftwalk out.
just to make sure you or an ally doesn't die.
lets you get back to your turret when you need to defend it or get to an enemy turret while your minions are there, (when doing that always teleport on the minion being shot at by the turret
only really helpful in the begining but it is extremly helpful in the beginning.
same reasons as flash except you can also chase them with this and get to a lane/gank faster with this.