There exists an ancient order originating in the Ionian Isles dedicated to the preservation of balance. Order, chaos, light, darkness -- all things must exist in perfect harmony for such is the way of the universe. This order is known as the Kinkou and it employs a triumvirate of shadow warriors to uphold its causes in the world. Akali is one of these shadow warriors, entrusted with the sacred duty of Pruning the Tree - eliminating those who threaten the equilibrium of Valoran.

A prodigal martial artist, Akali began training with her mother as soon as she could make a fist. Her mother's discipline was relentless and unforgiving, but predicated on the fundamental principle: ''We do that which must be done.'' When the Kinkou inducted her into the order at the age of fourteen, she could slice a dangling chain with a chop of her hand. There was no question - she would succeed her mother as the Fist of Shadow. She has had to do much in this role which others might find morally questionable, but to her it is in service of her mother's inviolable doctrine. She now works with her fellows Shen and Kennen to enforce the balance of Valoran. This hallowed pursuit has unsurprisingly led the triumvirate to the Fields of Justice.

Akali is OP, what else is there needed to say?
Although most poeple say you do not need skill to be good at Akali, but what if you did? Yes, you'll be beyond OP. So this is my way of building Akali.

These runes and masteries activeate your passive at level 1. The flat damage marks and offensive mastery tree branch gives you your lifesteal passive. This is gives you great lane sustain.
The flat ability power runes activate Akali's second passive, bonus magic damage to your basic attacks. This greatly increases your damage output and makes last hitting much easier.

Q-Akali's "Q" is what she uses all thoughtout the game. Her "knife and butter" as some poeple like to call it.
This is great for farming and harrassing. When you throw it, it also marks your enemies, so when you throw it at them, they'll be forced to retreat of lose a chunk of HP.

W-Akali's bubble as I like to call it stealth's her. It also gives her armour and MR. Her godly escape tool.
Use it when you are harrassing to slow them and strike the mark your "Q" put on them and farming upclose in melee range if your lane is pushed back.
This slows enemies and stealths you, making escape easy... no need to say more.

E- Most useless but still useful ability. Purely for damage and is best if used when in champion fights to conserve your energy. Easy to use small AOE ability and good for farming if needed.

R-OMG, probably one of my favourite abilities. This uses the "essences" you store, with a max of 3. This makes Akali so mobile. She can close in from great distances by using minions and great chasing ability... and KSing. 3 jumps, I mean, what else do you need?

With flat armour runes you should not be squishy at all early game. Normally by getting boots and pots are great, though I tend to sell all 3 pots late game cause Akali's passive makes her great at sustaining anyways. Dorans blade is a popular choice for those without runes. Some even get an amplifying tomb and a pot, all depends on what you want really.
The passive gives you only 9-10% spell vamp. With the hextech being nerfed, and unique spell vamp, you only gain 5% more, but you still get alot of AP from it! And it still builds into the gunblade and the slow is pretty nice from it.
Rylai's is a must. Akali without a Rylai's miss out on so much. AP, Slow and HP. Slow also helps you get that second hit on her "Q".
I play AP Akali, and not really AD, so I get deathcap, but some might want to build trinity and guinsoo if you want more AD.

Flash-Great escape mech along with your "W". Flash over walls or whatever.
Ignite-First Blood, kills poeple like mundo and poeple u cant be bothered chasing.

Other Viable options:
Ghost-Not really... you dont need the speed unless you're running away, early game, ok, lategame if u run it means your team is losing and most likely to lose anyways. if i made sense.

Smite-Jungling akali is pretty slow imo, but works.

Teleport-Suprise ganks and good when you need to back and get to team faster.

Exhaust- When other team is heavy AD or if your team needs it (which they shouldn't anyways cause you burst down their carry so yeah and u have rylai for slow)

<3