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Not Updated For Current Season
The masteries shown here are not yet updated for the current season, the guide author needs to set up the new masteries. As such, they will be different than the masteries you see in-game.
This build has worked miracles for Jax whenever I play him. Not only do you end up with insane dodge chance and damage, but you can carry a team and pretty much tank anything that comes your way.
First of all, I'd just like to note that the summoner spells are my own personal preference. I like the mobility of teleport, and exhaust helps greatly in taking down enemy DPS (Not that you need it that much with your dodge chance and stuns) or chasing down anyone who tries to run away. As for runes, those are your own personal preference as well, though I'd highly recommend evasion, attack speed, damage, or critical strike runes, in that order of priority.
My masteries look like this:
Defensive Tree: 9
Hardiness - 2
Resistance - 2
Evasion - 4
Nimbleness - 1
Offensive Tree: 21
Deadliness - 3
Cripple - 1
Alaricity - 4
Sorcery - 3
Sunder - 3
Brute Force - 3
Lethality - 3
Havoc - 1
Early game, buy your scepter, then farm like crazy. Last hit creeps, and if the opportunity arises, leap strike an enemy champion and stun them with Counter Strike, then exhaust once the stun wears off. You should be able to kill a champion from roughly half HP (more or less depending on what you're up against) by doing this. You should be able to lane for a fairly decent amount of time with the help of the life steal; once you're about level 6, you should have raked in enough cash to, at the very least, have gotten your boots and a recurve bow. If you don't think you'll make it because the enemy champions are shutting you down with harassment, you should switch lanes.
By the time you get your sword of the divine, you should already be dealing some fairly hefty damage with your ultimate, the passive, and your attack speed. But just to really stack it on, save up for the B.F. Sword of the infinity edge and get that next. Also, grab the lizard buff whenever possible. The burning damage and slow make you a frightening force to deal with. If you really want, you can grab the golem buff, too, for cooldown reduction.
End game, once you're working on your phantom dancer (Or banshee's veil if you've done particularly well for yourlsef) and you're about level 16, you should be unstoppable in melee combat. Between your lethal DPS and evasion and stun, even the dreaded Master Yi will be running from you. You may not deal as much raw damage, but your stun and dodge will easily put you on top in terms of survivability. Even so, don't get cocky and try to go in over your head. Pick your fights wisely with your team. You probably can take two or three enemies at this point if you play smart; go for the strongest damage dealers first, and exhaust any secondary target you run into, but only if they're a melee fighter.
-If you're fighting another Jax or are blinded, remember to use your sword of the divine's active ability to give you 100% hit chance and armor penetration.
-If you are fighting a caster-heavy team, you may wish to get Banshee's Veil before infinity edge.
-Against champions particularly good at harassment, such as Teemo, coordinate a gank with your team. It's better to suck it up and be humble early game than get shut down in its entirety.