Pros:
- Great damage early game.
- He can get quite tanky, even though he buys damage items, due to his passive.
- If he gets fed early game, he can be unstoppable in mid-late game.
- Can be build quite versatile imo, though he has some core items.
- Has some nice escape mechanisms (doge, stun, jump to a allied minion)
- A decent farmer, due to his high AS and his E-ability.

Cons:
- He lacks AoE damage and only has CC, if he dodges.
- He can be a bit useless in teamfights, if his isn't fed and the team isn't doing that well, compared to other melee champions like Xin Zhao & Mr. Yi.
- He is somewhat item dependant -> He needs Guinsoo's Rageblade fast, and also some survivability.

I always chose 9/21/0, like tank but.. jax is good when he dogde atak and stun so he have easy kill and he has extra dodge and extra movement speed on dodge is wonderful, and the extra AP and AS work well too. Strength of Spirit is surprisingly useful for staying in the lane longer. Basically, just take defensive masteries, you'll be glad you did. 9/21/0 is the way to go, making sure to grab the spell pen and CDR from the offensive tree.

all abilites is bassed on ap and ad, but jax ulty dmg is from ap, so i preffer ap penetration but u can mix runs with arp.Seals for dodge, from those masteries u got speed and with ability stun. I chose glyph for ap..as early as fight begin u will have extra from ap, and more powerfull skill so it's make easily first blood or then kills

i always chose Cleanse! i hate when i need just more hit and get blind stun or etc. it's also best way to run away(after cleanse use leap to near minion/champ)

Exhaust for first blood, or if u dont have all runes so make you not strong as you supose to do, but i also chose it for 100% chance to kill combine with empower and leap stike=no one can run away

if enemy are stronger on early or you dont have good teammate..i always combine Empower with leap strike and leap enemy. after u kill some of his hp, rush with this combo, exhaust and enemy has been killed! After leaping without meaning to kill him always run away some,or back to turret. Never go alone, only one thing can kill you it's yourself. Make trap or ambush from brushes, play like assasin kill or do last hit and run:)
Don't think you're invincible. I have this problem. All too often I do crazy things like running at fights my head knows I can't win, or chasing people way to far. Try to be cautious. Don't do stupid things. Yes you have a stun but you can't stun constantly, and if they slow you chances are their team will jump on you and you will die. Remember play to win not for score !!