Zed is a high mobility, high burst, melee assassin that excels at helping his team take care of a squishy target with relative ease after obtaining just a few core items.

Marks: I tend to take 9 Marks of Damage over armor penetration marks. The reasoning behind this is because the early game can sometimes be rough for Zed in certain lanes. Having the early AD over armor pen allows him to last hit easier and be able to trade better. There is no question that having armor pen reds is the better choice for scaling, but the flat attack damage helps a ton early.

Seals: I always take 9 seals of armor on Zed. Even if you lane against an AP caster, there will almost always be a marksman/adc on the other team so it never hurts. The probability of you laning against a ranged auto attacking AP will also be pretty high, so the early armor will really minimize their auto attack damage.

Glyphs: The 9 glyphs of magic resist are a no brainer, you will almost always lane against an AP in mid lane as Zed. These will help you survive longer and in turn deal more damage because of increased survivability.

Quints: For my quints I take one for Attack Damage, and two For Lifesteal. These quintessences allow you to not sacrifice a large amount of damage early, while giving you a surprising amount of extra sustain from the lifesteal in lane.

For my masteries on Zed I take 21/9/0 notably putting 4 points into sorcery for the cooldown reduction, and adding 0 points in defense to hardiness. The reason these are both notable choices, is because some people prefer to put 4 points into fury instead of sorcery for the bonus attack speed. The reason I think the CDR is better than attack speed is as follows: 1.) You get 40% from Blade of the Ruined King which is a key component on Zed, so the extra 4% is abysmal. 2.) There aren't many items outside of the brutalizer that provide cooldown reduction and make sense on Zed.

Addressing the defensive side of the masteries.
The fact that you scale much harder per level with bonus armor as compared to magic resist on Zed is the reason why I take all 3 points in Resistance in the defensive tree.

Blade of the Ruined King it the most essential item to get on Zed. While your ultimate Death Mark is active, you can use the activate of BotRK to add bonus physical damage dealt, and percentage health damage, which will directly add more damage to your ultimate.

Pros: Extreme outplay potential, especially with his new ultimate.

Great scaling and ability to assassinate high value enemy targets.

Fantastic wave clear, allowing him to farm wraiths with ease.

Energy champion, allowing for ability spam in moderation.

Great splitpusher.

Cons: Moderately high skill cap as indicated by his overview on the client.

Not the greatest champion at coming back from a deficit.

Fairly item dependent.
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It's important to note that this itemization and overall strategy to playing Zed has been deemed the most effective by myself after playing him and watching others do so. If you prefer another method or think mine is flawed, please leave feedback as i'm only trying to improve the quality of the game for inexperienced Zed players.