This section will expand on the item section above in more detail. It will provide more insight as to when and why each item should be purchased over the course of your game.
The item that ties the build all together. You have to get this every game, and you have to try and charge it as fast as possible. Always remember to toggle this item on and off depending on what you are attacking.
In most situations you will take these.
Mercury's Treads are the boots which are generally taken in most situations. The mix of tenacity, speed, and magic resist work great throughout the game. As a melee auto-attacker, it is important that you avoid being CC'd as long as possible to ensure you can auto-attack in the few moments when you are within range.
Take these if enemy team is heavy in AD champions.
Ninja Tabi can be taken in situations where you are constantly getting harassed by auto attacks or physical damage. The damage reduction from auto attacks is very helpful when dueling, or when assassinating AD carries. Just remember that you still need to get tenacity somewhere else in your build (which you can get from Zephyr).
Attack Speed Items
The standard attack speed choice.
Wit's End is the most common attack speed item I generally purchase. Kassadin can make good use of all of the stats on it, and it's relatively cheap to build. The bonus magic damage per hit synergies will with his kit. It provides a bit of magic resist to keep you beefy against magic damage. The scaling magic resist is actually very cost effective if stacks remain high: which is comes naturally due to the amount of auto attacking you will do with this build.
Take this if ONLY if you took Ninja Tabi for boots.
Zephyr is another quality attack speed item which provides a good mixture of stats. The reason you would go for this item over Wit's End is in the situation where you didn't buy Mercury's Treads. Zephyr is one of the few other items which provides tenacity, which is a vital stat to melee DPS champions. The bonus cooldown reduction and attack damage are more free stats.
Use this for EXTRA damage if you're snowballing. Not a CORE AS item.
A very controversial item. Many people consider it strong, while others consider it a noob trap. I was skeptical at first, however, this item actually exceeded my expectations. It's considered bad because it only works for 3 attacks, it can be CC'ed through, or even flashed away from. I also thought that it was terrible on melee champs, as getting multiple attacks against mobile opponents can be quite difficult. Kassadin does not have these issues, and here's why: through a built in silence, and two forms of slows (Force Pulse + Phage/Gauntlet), Kassadin can quickly and easily perform 3 devastating auto attacks without them escaping. No longer will Shacos, Ezreals, or Katarinas be able to flash away from your melee damage.
Good all around item. Get it early to never die in lane.
With the changes to to Season 3, Warmog's has quickly become a favorite due to its superb cost efficiency. Getting this item early also makes you relatively unkillable in lane, due to the large amounts of health regeneration. Having tons of bonus HP also helps make your innate passive more effective, allowing you to take more magic damage and gain even more attack speed. Try to get this earlier in the game rather than later.
One of the best defensive items. Armor, health, and MR. Don't forget the aura.
Aegis and Bulwark have turned into powerhouse items in Season 3. Bulwark is one of the best items for generating effective health vs magic damage. It gives a whopping 60 magic resist and 400 health. Let's not forget 30 extra armor and free health regeneration. Even if your team already has one, the auras can still stack between those who have one individually. Great all around defensive item.
The best defensive item against AD. Mixes HP and armor.
Randuin's Omen is known to be the bane of many AD Carries, more so than even a Thornmail. Randiun's provides the single most effective health vs physical damage. This is because it provides a large amount (500) of bonus health, along with 70 armor. Both the passive and active effects are also super strong at helping you disrupt team fights and chase down squishy targets. Getting hit slows the attacker's movement and attack speed. It's pretty scary when an enemy Kassadin Riftwalks into and uses the Randuin's passive to AoE slow the entire team.
A good choice if against anyone with scary spells (Blitz, Morg, Lux, etc)
Banshee's Veil is a good pickup because it offers three useful stats: health, mana, and magic resist. The Catalyst is also quite strong in early laning phase, offering you a bit of health and mana regeneration every time you level up. The spell shield is very strong against certain champions and team compositions. Specifically, it counters poke champions, or champions where one spell can quickly turn the tide of a match. Champions like Lux, Blitzcrank, Nidalele, Morgana, are few to watch out for.
Get this if you didn't get Randuin's, and want Trinity Force.
Frozen Heart is quite a rare buy, but it is a very viable option. Get this against teams that have a lot of auto attackers if your team is having trouble fighting against them. All the stats are very useful to Kassadin, including cooldown reduction for more spells, and a large chunk of mana for a bit of extra synergy with Muramana. Generally, Iceborn Gauntlet is a better purchase, but always consider this item.
Good mix of utility and bonus damage.
Definitely one of the most unique items in Season 3. It provides a good mixture of stats, both offensive and defensive. The main reason to pick this item up is the combination of armor, and the Spellblade passive. The Spellblade attack scales very well with Kassadin's high base AD, and helps to keep your targets locked in place with the bonus slow and slow from Force Pulse.
Tons of single target damage.
While Iceborne Gauntlet provides a good mixture of defensive and offensive stats, Trinity Force is pretty much a pure-offensive item. Buy this if you want to deal tons of damage. The phage and slow procs, like Iceborn Gauntlet, will help lock down your target, but it is not reliable. Take this item if you need to focus purely on damage.
Never get these. These are items which may look appealing, but in execution don't work well with previously suggested items. That's not to say these items are terrible, however these items do not mesh well with those intended to be used within this guide.
Stacking items. While gaining and keeping stacks is actually pretty easy on Kassadin due to his mobility, these items are incredibly cost inefficient. Couple this with Kassadin's already weak early game, and you have a very weak and poor champion in your hands.
You already have a built in slow, AND a built in flash every few seconds. You should never need this item to stick to a target, and if you need extra health there are much better alternatives like Warmogs, Randuin's, or Bulwark. If you're having trouble sticking to slippery targets, try practicing your orb-walking or focus on Riftwalking to a better location.
Armor penetration is not a stat that you need, as much of your damage comes from your spells and your Muramana burn, which is magic.
Similar to the items above, Malady is a wasted item on this build of Kassadin. Malady would be strong if you decided to built a lot of AP, since the extra damage on hit scales with it. The magic penetration on hit is useful, but the item just takes up a slot late game when there are more attractive choices.