So I started playing Jax...

He's amazing :).

If you're looking for a champ that can devastate an opponent in a matter of seconds, then stop looking... Or go look at Master Yi's builds. But really, Jax is awesome. Why? Because his attack speed is incredible, without actually needing ANY AS items, due to his passive on his ultimate. Also, if you haven't already, I would go check out Vasarius's build on Jax, the LoL Mistborn (Hybrid) because it is a very effective and well thought-out build.

Pros:
+Passive allows for a "tanky" build
+Ultimate passive is amazing
+Damage output is incredible
+Great ganker
+Great DPS
+He uses a lamppost to fight

Cons:
-Not a great farmer
-Targeted by enemy team
-Illusions of grandeur
-Can not initiate well

I went with a 16/14 mastery build on Jax. Why, you ask?

I feel like this is a pretty basic mastery setup. Jax needs that defensive boost in order to function well, because he will die fast if you're not careful. Vasarius suggests going more heavy on the defensive masteries, however, I also feel you can't ignore the extra armor piercing, or the extra attack speed. And obviously you will need the dodge boosts from the defensive masteries, seeing as how Jax's stun requires it.

But enough about masteries. Let's move on :).

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Alright, so the reason I chose this progression, is because in actual gameplay, it makes sense. You're probably asking yourselves why you would need two Hextech Gunblades, well, I'll tell you :).

Some people argue it's better to get a Lich Bane quicker, but I think that Jax can use the extra AD, AP, and boost from the gunblade. Besides, you can always sell it if you really wanted to. Now, you'll notice that Rabadon's Deathcap is missing from my initial build. FEAR NOT! I've found that I've never needed Rabadon's Deathcap so much that I would get it every game, most of the time we won before I could get it. So. If the game starts dragging on, and you're dieing more than you would like, go ahead and sell a gunblade and snag a deathcap. The extra AP late game will help you more than you know. Not only will it add lots of damage to your abilities, it will also increase your health a LOT. :D Now I'll go over why I chose the items that I did.


: Great shoes for only being 850g, adds some armor and the well-needed dodge that Jax needs. It's that simple.

Alternatives

: It never hurts to have some extra attack speed :) especially on a character that can thrive off of it.
: These are amazing shoes. I would suggest these every time. The tenacity and resist will help a lot. Get these if your game isn't going so well, and the enemy team has a lot of CC.

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: This is a MUST HAVE item for jax. If you don't get it, I will be sad. And so will he. Its passive is incredible, and stacks along with your ultimate, giving you ~2.1% AS by the end of the game. And with every third hit dealing extra magic damage... Aw yeah. :)

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: I've already sort of explained this one, but again, life steal, AP, AD, AND spell vamp. Yes, this weapon is a must.

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: I agree with Vasarius on this one. You get an awesome health boost, as well as some AP and the ability to slow down champs on hit, which allows you to chase them, and unleash your empowered-leap combo, which I will be going over shortly.

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: This will capitalize on your Sheen purchase earlier. It gives you a nice chunk of mana, your hits will deal a lot of burst damage, magic resist, and will give you some more AP, therefore, more HP.

: Jax's prowess with weapons and armor increase his fortitude as he gains equipment. Jax gains 3 health per point of attack damage, and 2 health per point of ability power received from items.

Jax's passive is one of my favorites. It gives him extra health so that you don't have to waste your money on health items. By the end of the game, you will have ~3.4k health, depending on how things go.
: Jax Leaps towards a target. If it's an enemy, he attacks, dealing 20/45/70/95/120 (+100% of attack damage) AND (+70% of ability power) magic damage.

This skill is pretty awesome. He leaps towards the enemy, lands, and busts their head open with a lamppost. Combined with Empower, this skill is a force to be reckoned with. It can also be used to get away, leaping towards a different target. Use it wisely.

: Jax charges his weapon with energy, causing his next attack to deal (60/95/130/165/200) (+40% of ability power) AND (+40% bonus attack damage) bonus magic damage.

The bonuses alone from this skill, even without the use of leap strike, are really good. It pretty much does what it says. If you use this + leap strike when an enemy is below 40% health, there is a 90% chance you will kill them on your leap. Using this to harass is a great way to deal a lot of damage in under 2 seconds. One... Two... PAUNCH! :)
: Passive: Jax increases his dodge chance by 10 / 12 / 14 / 16 / 18%
Active: Jax Stuns surrounding enemies for 1 second and deals 80/100/140/170/200 (+60% of ability power) magic damage to them.

Usable only within 7 seconds of dodging an attack.

Now the reason why you need the dodge is clear. If you can dodge ~30% of the time, you will be stunning often. Using this skill in battle to prevent them from running away, stopping an ult, etc. The only reason this isn't maxed earlier, is because 10% base dodge chance at the beginning is more than enough.

: (Passive) Jax's basic attacks increase his attack speed 6 / 10 / 14% for 2.5 seconds (max 10 stacks), and hitting the same unit 3 consecutive times enhances Jax's next attack for 140 / 170 / 210 (+70% of ability power) bonus magic damage

(Active) Grants 20/35/50 (+100% per dodge percent) magic resistance for 5/6.5/8 seconds.

In my opinion, this is one of the best, and easiest ultimates in the game to use. Obviously, because it's mostly passive. Yah, the active is fine, but the passive is really what makes you a threat. If you're having trouble with some mages, then by all means, activate it in battle, it will likely save your life. But the increased attack speed and extra magic damage every third hit are really what makes this skill great.

Now.

Maxing out Leap Strike ASAP is a must. Obviously, get Relentless Assault when you can, because the second you get it, you're a killing machine. Also, once you have maxed out Leap Strike, go ahead and max out Empower, but don't forget to shove a point into Counter Strike, because you'll need it early game.

Your bread and butter combo will be the empowered-leap. What is this, you may ask? It's simple. You use empowered, followed by leap strike. The best part is, it resets your auto-attack. So you'll get in an extra auto-attack when you land :) YAY! Possibly dealing more magic damage, due to your ultimate. And all the while, increasing your attack speed :D.

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Flash: The reason you want flash, is so that you can easily give chase if your prey tries to get away, or, you can simply flash away to save yourself. Flash is easily the best summoner spell in the game.

Exhaust: Exhaust is included for the same reason. You can exhaust your enemy so that they can't get away, and you can simply kill them with an empowered-leap. :)

Alternatives

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Ghost: Ghost is a pretty strong alternative. Lets you run away with ease or catch up with someone, ignoring physical objects.

Teleport: Teleport is good for getting right back into your lane so that you can continue gained EXP and gold. It's also really good for helping out teammates, and teleporting when needed. This is my go-to if I don't use exhaust or flash.

Cleanse: Cleanse is a good summoner spell to have on hand. Especially if your opponents have a lot of CC. You can cleanse, and attack, or cleanse, and get away.

NEVER USE

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Revive: No. NONONONONONONO. NO!

Early Game

Early game, you're going to want to grab boots of speed, some potions (Or Doran's Ring/Shield if you're feeling confident ;]) and stay in your lane. IMO, Jax can take mid fairly well. He can keep the ranged at bay by leaping at them. Others would probably disagree with me. Which is fine. If there is a better alternative on your team (i.e. Annie, Ryze, Xin, etc.) then let them take mid. Otherwise, pick a lane. As usual getting last hits on minions is a must. You can easily harass the enemy by leaping every so often, and once you reach level 2, start throwing in an empowered-leap. Don't get too over-confident though, Jax is pretty strong early game, but he can also be easily killed. Laning with Jax at the beginning is EXTREMELY important. If you fail at laning in the beginning, you're going to have a really rough time doing well in mid or late game. At the very least, if you're doing bad at the start, still grab Guinsoo's when you can. Believe me, it will help you a bunch.

Mid Game

By mid game, you're likely strong enough to kill any squishy at full health in any engagement, assuming of course, that you play it right. During mid game, try to focus on helping out your teammates, and you can grab the Red buff ASAP, it will help you a lot. You should have Guinsoo's Rageblade by now, which is why you should be killing quite a bit during mid game. Again, Jax is not a tank so be extra careful. Wait for late game, when you can tank most things, given your very high attack speed, and leech.

Late Game

In late game, you are unstoppable. Well, almost. You have most of your items, a ****ton of health for a non-tank, and you deal an absurd amount of damage. In teammfights, make sure you NEVER initiate. If you do, you will die. It's that simple. Focus on killing the squishies, because you can just leap past the tanks, and decimate the support, while the rest of your team keeps the rest at bay. Be sure to apply empower at every chance you get, and leap if you have to. Also be sure to CONSTANTLY spam counter strike, the stun, will save your life. You want to make the most out of your spell vamp and leech. This is why I included the extra gunblade, totally worth it.

This is my first build, so be nice! ^-^ Kidding. You can say whatever you want. But please use the build before voting, and leave comments so I know what to change! I'm very good about considering suggestions, so please feel free! I will update this often, given the reviews and suggestions.

Thanks! And happy playing!

9/9/11: Added more to Early Game section
9/9/11: Switched from Doran's Ring to boots and potions
9/9/11: Modified Mid and Late Game sections
9/16/11: Switched some item descriptions around
10/26/11: They have since nerfed Hextech Gunbalde.