Hi and welcome to Jax, The Hybrid Machine.
In this build i mainly focus on ability power but joining with a bit of attack damage. I believe that Jax should have some attack damage so that if after you use your combo, you can take some more damage from your enemies when you're abilities are on cooldown.
Notice that thanks to his passive, Jax does not need to buy many health items.

The choice on the Greater Quintessence of Evasionand on the Greater Seal of Evasion his pretty obivous but i will explain anyway. It's for dodge chance to give a greater use of your Counter Strike.
I choose the Greater Mark of Magic Penetration so that you Leap Strike and your Empower have a better damage and the
Greater Glyph of Ability Power so that all your abilities have a greater damage.

I choose to put those 21 points in Offense so that Jax can have the damage he needs when your abilities are on cooldown and when you use them. It's also so that his magic penetration and armor penetration is bigger.
Those 9 points in Defense are so that he can old his lane and so that you can get to your lane faster in the case of your enemy pushing to much.

Pros:
+ One of the best fighter's around.
+ Jump everywhere with Leap Strike!
+ Do well if your team is average.
+ Counters tanky DPS quite well as he gets frighteningly strong the more he battles
+ Wonderful passive, allowing him to take the brunt of any carry's damage
+ Excellent pusher
+ Great DPS with Guinsoo's Rageblade and Relentless Assault stacking attack speed

Cons:
- Can do 1v1 very well, but 1v2+ requires caution.
- Crowd Control is a real pain!
- Bad farmer untill level 6.
- His combo is countered by Banshee's Veil since it's passive will block all the damage from your Empower + Leap Strike
- You run out of mana easily on early game
- If you fall behind its very hard to catch up again in terms of levels and kills.
- Able to be picked on by ranged early game

Relentless Assault
Jax's prowess with weapons and armor increase his fortitude as he gains equipment:

Jax gains 3 Health per point of Attack Damage received from items.

Jax gains 2 Health per point of Ability Power received from items.


Leap Strike
Jax leaps toward a target. If it's an enemy, he hits the enemy for 20/45/70/95/120 (+) (+0.7) magic damage.


Empower
Jax charges his weapon with energy, causing his next attack to deal an additional 60/95/130/165/200 (+ ) (+0.4) magic damage.


Counter Strike
Passive: Increases Jax's Dodge chance by 10/12/14/16/18%.

Active: Jax stuns surrounding enemies for 1 second and deals 80/110/140/170/200 (+0.6) magic damage to them.

Usable only within 7 seconds of dodging an attack.


Relentless Assault
Passive: Jax's basic attacks increase his Attack Speed by 6/10/14% for 2.5 seconds (max 10 stacks). Every third consecutive attack deals 140/170/210 (+0.7) bonus magic damage.

Active: Jax's speed allows him to reduce incoming magic damage. For 5/6.5/8 seconds his Magic Resist is increased by 20/35/50 plus his Dodge percent totalling   Magic Resist.

I start with a Doran's Ring and aim right away for the Ninja Tabi for greater dodge chance (this is a must buy item when using Jax). Next i wanna get Guinsoo's Rageblade for the ability power, the damage and for it's passive. An item that you also must buy when using Jax his the Hextech Gunblade for the damage, ability power, lifesteal and speel vamp (lifesteal when you use abilities). The next item depends on the enemy team:

• If the enemy team does not have a tank, you should aim for Rylai's Crystal Scepter so that your enemies are slowed from your abilities and for more ability power. Then you should wanna get the Lich Bane for mana, ability power and it's passive: "When you use an ability, your next physical attack will deal an additional 100% of your Ability Power in damage. This effect has a 2 second cooldown.", and since the cooldown is so low you use this passive almost all the time. The final item is
Void Staff for magic penetration mainly.

• If the enemy team have a tank, you should get a Madred's Bloodrazor. Next come the Abyssal Mask so that you have ability power and so that your enemies have less magic resist. I believe that Madred's Bloodrazor and Abyssal Mask are a good combo because the Madred's Bloodrazor makes your "basic attacks deal bonus magic damage equal to 4% of the target's maximum health". The final item is Lich Bane for greater damage after the use of an ability.

I believe Flash and Ignite work very well with Jax, since the Ignite let's you finish off the enemy champions faster and the Flash let's you get close to them easier, or if they try to escape.

You can also use Exhaust instead of Ignite if you prefer to try and get kills from your enemies faster.

Ghost is also a good choice if you think that your Jax doesn't not need Flash. Ghost also let's you get to your enemies faster or if your enemies are pushing or you need to help a teammate, Ghost may let you get to him faster or get to the turrent where they are pushing faster.

I hope this build help you get a great score with your Jax and so that you can easily go off-tank.
Vote, comment and say what i need to improve in this build.