So this is all about maxing out critical chance & damage. With this exact build you hit 100% critical chance along with over 300% crit damage (once you factor in Lethality ), after that your damage is over 840, all the time. Also by buying in the correct order you can stay competitive through the early game, and Burn through everyone mid and late game. This build also offers high attack speed and movement.

Avarice Blade, this sword makes paper. It will help you pay for this expensive build. If you are afraid of crowd control buy Mercury's Treads instead of Berserker's Greaves. Once you have bought Zeal and footwear, you need to ask yourself one question: Do I feel lucky? If you plan on not dying after this point, buy Sword of the Occult and continue with my item build excluding Black Cleaver. This is the less expensive option and it offers a maximum of 55 more damage. If you have been feeding already, buy the B. F. Sword. When you come charging back into your lane the enemy will notice the extra damage. 2 Phantom Dancer + 1 Infinity Edge = Win, This is the core of the build. With just those three purchases you're buying 85% crit chance and 50% more crit damage. Black Cleaver offers good attack damage and speed as well as some armor reduction. Turn Avarice Blade into Youmuu's Ghostblade after you have the gold. This is the icing on the cake. Youmuu caps your crit chance, reduces your cooldowns, adds some armor pen, and gives you a great extra ability.

Ignite is great for tanky enemies and will help you to kill those who know when to run.
Smite is a good choice for jungling, can be switched with Cleanse which will help you with crowd control. It can get scary when your enemies are saving up their stuns just for you. Teleport is good for wanting to seem omnipresent, Ghost is good if you want to be a gold medalist sprinter, while Flash is for people who understand Flash.

FUROR! All the way! It's kinda the point. Best defense is unrelenting offense. If you just disagree, by all means stick to Greater Seal of Armor and Greater Glyph of Magic Resist but Greater Mark of Critical Damage and Greater Quintessence of Critical Damage is where the party's at.

Let's say you arn't level 30 yet. You can afford to max out Lethality at lvl 19. This gives you that extra 10% of crit damage.

I don't really pay that much attention to the order myself. Alpha Strike is important to have at the get go, you will use it to creep/jungle/farm, and will usually get maxed out first. Wuju Style is key to winning one v.s. one, so don't neglect it. Meditate will keep you going when times are tough. Highlander is great when you want to see an enemy rage quit.

Pros:

high powered DPS paired with fast movement allows for excellent backdooring, jungling and killstealing j/k.
All Items complement each other for maximum efficiency.

Cons:

Expensive Item build works best with long games.
Squishy Master Yi needs both care, and confidence in combat.