You can play jax as: AP, hybrid and AD.
I played him always as hybrid, but i wanted to try somthing else!

Please Don't Rage, or flame, this is my first guide.

Why the bloodthirster? Because: Lifesteal and AD + The bonus = 20% lifesteal and 100 AD
Why the Black Clever? Because AD, Attackspeed and the armour Pen.
Why PD? Because Attackspeed and Movement speed.
Why the Frozen M? Because Health, and AD.

I choose these Masteries Because: AD, Lifesteal And damage on turrets.

Ghost = good for chasing.

Ignite = just a good spell

Farming is important for the BT Stacks.

And for cash ^_^

Pros:
short cooldown on empower
Good Dodge
AoE Stun
His ult grants you Armour And MR
SO MUCH DAMAGE

Cons:
-nothing for me

Leap Stike: (Active): Jax leaps towards a target, dealing physical damage if the target is an enemy.
Cost: 65 mana
Range: 700

Empower: (Active): Jax charges his weapon with energy, causing his next autoattack or Leap Strike to deal additional magic damage. This ability resets the autoattack timer.
Cost: 30 mana

Counter Strike: (Active): Jax enters a defensive stance for up to 2 seconds, dodging all incoming basic attacks and taking 25% less damage from area of effect abilities. At the end of the duration or if Counter Strike is activated again, Jax deals physical damage and stuns nearby enemies for 1 second. This spell deals 20% additional damage for each attack dodged to a maximum of 100% increased damage.
Diameter of AoE: 375

Grandmaster's Might: (Passive): Jax deals additional magic damage on every third basic attack. The counter will reset if he does not attack for 2.5 seconds.
Magic Damage: 100 / 160 / 220 (+0.7 per ability power)
(Active): Jax gains armor and magic resist.
Cost: 100 mana
Duration: 8 seconds
Cooldown: 80 seconds