Well, This is my Jax OP Build, sometimes it can be hard to get it, Since you could get ganked alot, or die alot, but in the end, You'll easly win, if you follow my Guide.

The following items we will be using:

My friend gave some items for jax, And in the end, I came out with this, And I won every-game with it, if you got proper team mates. Even if you die alot Early-game, In the end, you will be there. Then it doesn't matter anyway.

I came up with the perfect runes, Attack speed, for early game,+ Replacing Atk speed items.
You do not need that much atk speed anyway, Because once you reach level 9 You will have rage-blade, And perfect Farmer.

Marks-

First perfectly with the Masteries, and your [W] [Q] Combo, Gives you great magic penetration.


Seal-
Obviously Dodge, Works Perfect with [E] And makes Jax a good surviving Class.


Glyph-
Great for early game farming, And replacing some atk speed items for beginning game, In the end you wont even need Atk speed items, With Rage-blade and Your ulti.


Quintessence-
Obviously Dodge again, Since you cannot buy dodge in the shop ( Only shoes) And it will make it awsome for 1vs2 Or even 1vs3 If your good feeded. ( In the end you would have 43% Dodge)

I Choice for these Masteries, Since Jax doesn't need Offencive Masteries, It's better to get them defensive, Since you would really need those Masteries for surviving after fights or even In a fight. Afcourse I also selected Magic Penetration, for your Magic spells.

Sorry if it looks abit messy, But I placed the exact order of Items in the list.

Total you would get just These items.
Normally I used to pick Atma's Impaler, Then you would have In the end 300 Attack damage, and over 500 Ap, But The thing is, Lich blane fits better for it, In my opinion, Since you wont need damage anyway, With your skills you nuke them away.

Most of the time, I first buy Deathcap, Then Rylai's Scepter, Because I actually don't need HP that bad, And I got enough AP, But, If you get killed alot, or take alot of damage, First buy Rylai's Scepter!

The skill order is pretty clear,
I buy the leap at level one for first blood, Escaping.
Then I buy Empower to attack Minions, Or Enemy's with it. It's pretty handy, Since you can just W, And then Q And you just walk back again, and hunt minions down..

Then afcourse Stun, And then already without boots you would have Over 20% Dodge.

And then I max out Empower as fast as possible, Then level Dodge/ stun To level 3 orsomething, Then I Max Leap. Then Stun.

Most people use Exhaust flash. I used to do that most of the time too.
But after a while, you won't need Exhaust anymore anyway, It only saves your *** sometimes. Then I found out, Ignite, is the perfect Summoner spell to early game get kills. And later to fight in huge battles, finishing off multi-ply people. And Afcourse, Always get flash, To flash out, then Use Q To swing to another minion, so basicly you use Flash twice, Wich is great. to survive.

Once you reached level 18, You should have Total Over 43% Dodge, Wich is great, since you just walk into the front of Minions, till you recieved stun, then you jump onto him, Afcourse with the [W] [Q] Combo, Then you wait for him to hit back, if not you ignite him, and keep using the combo on him, To afcourse finish him off. You could always use in early game, via the brush the combo, To Just jump into him, and walk back in the minion field, and then fight- Wait for them to come back again, and suddently jump onto them, and Ignite, Would give you a kill, Wich is so great about Jax.

Once you reached Level 7 You should Kill each time in the jungle the small monsters without buffs, Only from your side. Then get back in the line, Till your level 9, And you could do the boss, Then you get rageblade, Then make sure you keep the line perfectly of minions in the middle, and get the jungle Empty. If you keep doing that, You will easly win. And perfect gank. It's the best method I've seen, In 3vs3 This Method works so good, I always do it, And Most of the times, I win ( Depends on my team mates)

If your in the same line with an mage / Distrance against you, make sure you stay behind the minions properly, And if you think you can engage the Minions ( Only the one with Low HP) Then Hit them till their dead. Make sure you hit them on the most Low HP, So you recieve the cash.

If you the enemy is doing to much distance attacks, make sure you keep his HP low, so keep attacking him and walking away, Then the Distance class won't come close, Since he knows you can jump on him, Then you can easly farm it all.

If you do try to use this Build in ranked play, Wich can be done perfectly. Make sure, you get Rylai's first, before Deathcap, Or even If you get attacked alot, before lich blane.

After I took the jungle with me, And bought some Buffs from the Shop( Atk speed, hp, AP) I Walk most of the times ontop, And wait for them to attack, if you are with an group, Make sure you keep attacking some one, no matter what, make sure you keep attacking the champions! It will heal you so hard! That's why I selected Gunblade for it. Most of the times if I keep fighting, I won't even die Even if I almost died at the beginning. And try to stun as much as possible, Keep using all your skills all the time!