Jax is a great champion he can play different roles in a game,he is the best 1vs1 champion,he is very good at doding and stunig XD

PROS
+ Great damage early in the game
+ Great carry
+ AoE Stun
+ Easy to learn
+ Good farmer
+ Can get hard to kill due to his passiv

Cons
- Focused in team fights
- His stun only works when he dodges
- Can be easily shut down by crowd control effects

I get Ignite and Exhaust
Exhaus good for chasing and it can be good for running away
Ignite is good for 1vs1 combat and is good for geting last hit on a champion who is running away

Start off with a Dorans Blade

Then buy Ninja Tabi these boots are great for Jax it gives you a little armor and 12% dodge

Third item is Guisoo's Rageblade this is a must have item it goes well with you ulti and it gives you AP and AD

Then i go for a Phanton Dancer you dont need to get these but i get it becaus i love the extra mobility and Crit

I then buy 2 Hextech GunBLades becuse the give you everything you need it gives you AD,AP Life steal and Spell Vamp it's overal a great item to have on Jax!

Well i want all of my skill's too be on the same with jax but i max out Leap Strike First

Well this is it hope you like it XD