If you want to know why I still use Hextech Gunblade then go to the "Things you should know" section.
Now this is guide for the first Jax build shown above, the second one with the warmogs I do not use normally and there for can't do a guide to go with it.

In this I may link to top guides of characters just to show you who I'm talking about if you don't know and link the skills.

Apart from most guides this is one of few that use Sheen, it is also the only one of those few that use Atma's Impaler, Rylai's Crystal Scepter and Trinity Force all together

Now Jax may be powerful but he is not a tank. Simply do not jump in to a load of champions and expect to beat them all. You are an assassin with him and should jump at unexpecting people and kill them. With Jax always remember to use your active Hextech Gunblade. This slows and helps Jax catch up with enemies.

This is a hybrid build. This means very nasty and it will make you enjoy Jax using AP and AD.
Now before I go to deep I want to point out that Jax is slightly difficult to play. This may be your first time with this build so don't expect to win. Now on to physics.

Now I choose Greater Marks of Strength , to make Jax's damage larger and it will make them afraid of you early game which is always a good thing. This is also used with the Greater Quintessence of Strength.
I chose Greater Seal of Evasion to make Jax's Counter Strike affect easier to use. This is not to be underestimated as the spell can win you battles and help you get away when the need arises.
I chose Greater Glyph of Ability Power because Jax's spells are mostly AP and why not as we are getting Rylai's Crystal Scepter ?

Masteries are heavy on attack because it will make you do far more damage and you will rule early game. Masteries are unfortunately underestimated and not used until higher levels. This is not to be the case. Masteries are powerful and greatly help.

I have found myself killing other Jax's just because they are too lazy to use masteries.
You may be level 30 and have all your masteries and in that case you won't find other people without masteries as most level 30 see the importance of it

At early game, you may find it hard to farm if you are against AD ranged carries, and you should not try to despratly farm by going in which would probably get you killed.
If you are fed early game, then you will dominate late game as well. If you are not fed early game, you battles will do fine but not with Jax's full potential.
Also, a Hextech Gunblade nerf isn't a ground bringing nerf and it should still be used.
Roit are reasonable with nerfs and buffs, through if you haven't played to champ that they buff, you might not see the full picture, so Hextech is still a good item.
I have found people playing as Jax without Hextech Gunblade of late and found them losing like anything.

Before I start please no comments about getting Sword of the Divine , it's Jax's counter not helper and can be exchanged for much better items like Rylai's Crystal Scepter .

Items:
You may see that in the items section above it shows items but not what builds to them, feel free to build up to them when to get to them

Now starting of with a Doran's Ring really give you that bit more hitpoints you need and a bit more mana regen to help you not have to recall all the time for more mana. You may swap this for Cloth Armour and two Health Potion and a Mana Potion .

The Ninja Tabi comes next. This really helps Counter Strike and gives armour as well as speed the retreat and chase, this should not be sold later even if things are looking desperate and gives more dodge chance .You may want to use a Berserkers Greaves instead but only for dominion.

Sheen gives the mana you need and has a neat passive to do more damage. This is used to build to Trinity Force . Note this has been edited.

Get the Hextech Revolver or the Bilgewater Cutlass before the Guinsoo's Rageblade which will prepare you to buy the Hextech Gunblade .

Now the Guinsoo's Rageblade is good in working with your Relentless Assault and give that extra damage making mid to late game easier, now some people may not want to buy this and get Phantom Dancer . Don't get Phantom if you are facing another Jax

Then the Hextech Gunblade . The Doran's Ring can be sold here in order to help buy this as when you get it you can be tankish with more health and it active can be deadly.

Get the Atma's Impaler here. this will makes the more hp you get also be attack and since attack increases Jax's health with its strange to think why it doesn't go one a infinite loop and continue to increase Jax's health and attack

Rylai's Crystal Scepter just give more ability power and health making Jax completely unstoppable.

Then get Trinity Force

also remember to buy elixirs at the end on the build to buff up your character

Now I probably bugged up the skill sequence but I know to get Leap Stike first then empower and counter strike. Then focus on leap strike until you get your ult, then go for empower and leapstike only upgrading counterstrike when you have to. in my opinion counterstike is a one point wonder. always upgrade your ult when possible and remember to use it against people like veigar to stop their ult causing so much damage through a Veigar ult will still do a lot of damage.

Yeah I always pick Flash because who wouldn't?
And Ignite is good early game to get kills.
of course Ignite can be trashed for Teleport but only Teleport or Exhaust but I seriously like Teleport cause you can alway get back in and get xp all the time
if you take Teleport or Exhaust take the point out of upgrading Ignite and use it in something else

* always target weak champions and try to gank as much as reasonable to build up kills
* if things are not looking good switch lanes with a friend
* start tower diving at level 7 but don't be overconfident of Jax's abilities
* if a enemy is overpower early game and mid game, that doesn't mean you can't beat him late game

* never be in a lane with a heavy harasser like Brand, a fire champion for those that don't know
* never surrender, remember there is always a chance of winning even if things look bad

Really? Seriously?
Now Jax is better of in a lane getting kills so no jungling except if you are going badly in a lane.
you can farm easy in the jungle once you get your AoE stun spell and that will help you take out the lesser creeps, also your AoE can help you team kill Baron Nasher, to top Jungle creep, by stunning him, through I don't know if it works as its hard to tell when everything is trying to kill it and chaos reins

Try to get as many lane creep kills as possible but don't take risks just to farm, chase of the enemy with leapstrike and the AoE stun until they have to go back and then farm as fast as you can. Jax can easily push a lane and dominate dragon solo at level 10 or 11

Jax is fine with Ranked play and will make you known for
skill, or just playing an OP champion and being a total bad- well you get the picture

Stick with your team even when there is a good chance of getting kills you need to hang back and help teammates that are in trouble.
if you are about to lose don't just run of to get a kill, stick around and defend
a good organised team is a happy one, 60% of the time....
if there is no tank or jungler on your team don't worry, Jax makes up for the jungler and he is a little tankish through the other part of the Jax guide which you can switch to up top is more tanky

Remember Jax is only OP if you play him like that. It all comes down to if you play him well, if he is your kind of Champ and if you build him right.
stay away from people like Blizcrank and Brand
it is always wise to be wary of Ryze and Morgana as they can easily trap you and let their teammates kill you

This build was from me(Jimbo) from the GopherGamming
please click the link below to view our page and like if you want
TheGopherGamming

Remember always stick with you team and don't start fights without them except one on ones.
Don't get focus heavily on lifesteal through we are getting Hextech Gunblade . I mean you can but attack weapons increase Jax's health with his passive.
always remember, Jax may seem overpowered but it how you play him and build him that makes the magic Of:
Jax: the grandmaster at arms
this was a Gopher gamming build, comments and ratings are much appreciated to make more people learn to play Jax like a boss
remember Please comment even if its negative cause I always want to hear updates and pointers