I'd just like to say, that if you go with my build, and play smart, I promise you will dominate.

I don't necessarily advise you to single lane with jax in the beginning, or atleast until you get to level 6. You can do whatever you want though, once you feel like you really begin to understand the way that jax works. Like the skill sequence says, I would really recommend upgrading leap strike and empower first, only because the combination packs a good punch, even for the beginning. If you face teemo, you can take a 1/3rd or 1/4 of his life, or anyone relatively squishy. After you power up those skills, the main thing to focus on is your counterstrike, or dodge. Not only does your dodge rate go up everytime you upgrade it, but it stuns your enemy, which really helps whether they're trying to escape or you are. If used with empower right, this becomes a deadly tool, forcing your opponent to stay put, while packing huge amounts of damage, especially with your every-third-hit critical, provided by jax's passive ulti

Hopefully by mid-game, you have the hextech gunblade. With the combination of the rageblade and jax's ulti(passive), you will accumulate much speed, the more targets you hit consectuively and with that, you will be a much better version of warwick, dealing out a lot more damage, taking in hp as you get depleted of hp. If by mid game, you only have the rageblade, it is dire to stay with team mates and gank when they gank. The more kills you receive, the faster you can aquire the above, godly items.

You should have Nashor's tooth and Warmogs Armor. Honestly, I sometimes don't even need Warmogs Armor. Nashor's Tooth for Jax is an under rated, overlooked item. it provides 55% Ability power and 50% attack speed, along with 25% cool downs and mana regen. This helps so much. Why? With the combination of your rage blade and jax's ulti(passive) it takes a few consecutive hits towards targets to accumulate speed, RIGHT? BUT!!! with nashor's tooth, you will begin automatically attacking at a high fast speed, which means the combo with rageblade and jax's ulti(passive) will allow you to attack even FASTER! At late game, things will start to get serious, and you will most likely encounter enemy champion after enemy champion. The 25% cooldown time and the mana regeneration will allow to keep owning, without needing to go back to base If you have warmog's armor, you are invincible....

I've already established the fact that Jax's dodge plays a huge part in owning. Sometimes to get the upper hand on an enemy champion, it is best to walk through a crowd of minions, just to trigger your counterstrike, as they will attack you. After it is qued, first use empower and then leapstrike your opponent, followed by counterstrike. You can own ryze, ashe, teemo, or anyone relatively squishy in literally two/three seconds if you do this, followed by using your hextech gunblade. Also, there will be times where you wlll need to run away from champions. If you are on the edge of dying with an enemy champion right behind you, you can use your leap strike on your own minions or fellow champions, to get the extra feet you need to safely return to base.

If you add up all the dodge percentage from the ninja tabi boots, the dodge from masteries, dodge seals and the dodge from jax's abilities. That is 37% dodge rate. That is almost 1/2 hits he dodges/avoids

If Lux, Pantheon, Tristana, Morgana or Anivia are on your team, they are your best friends. Lane with them. Double stuns are a great combo against enemy champions. Although Anivia cannot stun, she can build a wall, surrounding your opponent, giving you more take-down time.

Jax is called the grandmaster at arms for a reason. If he wasn't, he'd be called, "Grandmaster of ability" As ap/ad Jax I have gone against players who think it's a good idea to use AP Jax and have dominated them. The only benefit of going AP jax is that your abilities will do a little more damage than if you went AP/AD jax.If your abilities had zero cool-down time, than it would be flawless, but since they do, it's not a good idea, especially since jax is a melee fighter. Also, if you are AP jax, your ulti's passive, "every-third-hit-critical" would be useless, since Attack Damage is necessary. All melee fighters need attack damage. Since jax uses Ability Power AND Attack Damage, it is essential to equal out the ap/ad, which is why the build I have provided is so good, because it does just that.

I'm glad you asked. Leap strike, without any items that give cool down reduction, is 12 seconds, where as Counterstrike has a 4 second cool down. In the time given, you can do more damage, especially to surrounding foes(which is brilliant since you will be 1 on 2 occasions) and live longer if you upgrade counterstrike before leap strike.

I honestly can say that if this guide does NOT help you, then you should try one more time, or select another champion. The build and advice I have given you is far superior than anyone's I've read, believe me. I play nothing but Jax, and win most of the time as long as my teammates don't feed.