Jax: So awesome he was forced to use a lamp post in battle. He is the Chuck Norris of League of Legends, and he knows it. Jax is a must-have for every summoner profile, he will destroy any competition in seconds, win games faster than you can say "/surrender!"
With this Jax build, you'll have the other team begging for mercy within minutes. I built this for a 3v3, so it might work better as a 3v3 team, but lets face it, Jax rocks any team size.

I personally love Jax, he's a REALLY good champion, albeit overpowered. He's just fun to use, he's that mass murderer that you've always wanted to be (you know you wanted to). He's is an amazing DPS. This build is mainly DPS that leans a bit toward hybrid. So you get the best of both worlds.

I use Jax mainly for team battles, he can destroy 1 on 1, but if you get him in the middle of a team battle, your team will come out on top.

Oh yeah, you'll actually end up with A LOT more than 1900 health with this build. I was topping around 2700. Just to clarify.

Basic runes build around evasion and attack speed. Jax's ace in the hole is his dodge chance. By the end of the game, your dodge chance will be really high and you'll be able to pop your E just about any time you want to.

Masteries centering around evasion, and some around ability power. Jax gets health for ability power, you hit two birds with one stone. Jax's evasion chance makes him such a powerful champion, you can do all the damage you want, but missing 25% of the time isn't good for anyone.

Jax's skills:

Equipment Mastery: This is an awesome skill. He gets health for being able to do damage. This keeps Jax from being too squishy. It'll keep you alive, to say the least.

Leap Strike: I love this skill, only because it can be used both offensively and defensively. You can use it to run, or to push. As soon as you use this attack on an enemy champion, 98% of the time, they'll run off. Very good for getting in the battle, screwing someone over, and getting out. Use this often.

Empower: This skill is AWESOME. It gives Jax a HUGE punch as soon as it is activated. When I activate this skill, I rip the enemy champion's face off and laugh at them. Use this often.

Counter Strike: This skill give Jax some amazing dodge and an awesome stun. The stun is best used when taking on an enemy champion to turn the tide in your favor (It'll already be in your favor, you're Jax).

Relentless Assault: Jax's ultimate is more revered for its passive, not its active. Its passive makes Jax attack faster, and faster, and faster after each hit. Coupled with Guinsoo's, this is a deadly skill. Use the active if you're going up against a mage type champion.

It should go like this:

Doran's ring at the very start, the added AP is also a health boost. Win-win. The mana regen is nice and so is the health boost that comes with the ring.

Grab some Ninja Tabi, the evasion is very nice for Jax because of his E. Everyone needs boots.

The bread and butter for Jax: Guinsoo's, it's passive is PERFECT for Jax and as soon as you grab this beauty, the other team won't stand a chance.

I know what you're thinking: "Hextech Revolver and Gunblade? Why would I grab that?" The ability power boosts Jax's health AND it gives him some spell vamp (important) and some life steal, you get the best of both world's with this item.

Phantom Dancer, once again, I know what you're thinking: "Jax's ultimate gives me attack speed, I don't need this item! Noob!" Yes, you do. It helps you get 10 stacks in a snap AND when you get your 10 stacks, your attack speed will be maxed out.

The Bloodthirster, basic attack damage, and some more lifesteal, you'll be unstoppable in seconds with this.

Thornmail: Sell your Doran's Ring and buy some Thornmail, you'll make the other team think twice about attacking you. This item was put here to be mean. All's fair in love and war, but especially war.

Go solo, be by yourself and JUST farm. If another hero comes and messes with you, rip his face off and continue to farm until you grab your Guinsoo's. Then just destroy the other team by ganking and just being awesome. Jax is amazing solo, but he can be truly devastating when he gets power-leveled and fed.

Always, always, ALWAYS have something to hit if you are in a battle. Whether it be a minion or a champion, as long as you're hitting something, you'll be safe.

Don't get too cocky, never initiate a fight unless it's 1v1. You can 2v1 people, but it's best if you not, trust me.

In the beginning of the game, go and farm, and farm, and farm. Gank for some teammates a few times. Jax is amazing at ganking, just come up from behind, pop your Q and then W, and watch their health disappear. If you're taking on a group, you may want to wait on some of your teammates and then charge into battle. NEVER initiate a 2v1 fight as Jax, it will end in your downfall.

Pros:
He's awesome
He's awesome
He's awesome
He devastates 1v1
Super high DPS

Cons:
Players get cocky
If targeted, cannot do anything