Jax - Balanced Assassin, Hybrid and Bruiser Cost: 1350 IP or 585 RP Roles: Top and Jungle. Speciality: Tons of Damage. Lore: It is seldom the case where a champion is defined by his actions after joining the League of Legends rather than before. Such is the case with Jax, for whom the argument could be made that he is the most prolific tournament fighter currently at the Institute of War. For reasons known only to the former leader of the League, High Councilor Reginald Ashram, Jax was put on the top of the list of candidates to receive a League Judgment. Jax proved himself to be an immediate terror in the Fields of Justice. The self-proclaimed Armsmaster of the League rattled off a streak of consecutive wins that to this day has not been matched. A number of summoners in the League grew concerned that the perceived objectivity of the League of Legends would be questioned by the presence of an unknown fighter who was unbeatable. For this reason, the new leader of the League (following Reginald Ashram's disappearance), High Councilor Heyward Relivash, created special restrictions for Jax to fight under. This was something the League had never done before, and something which has never been done since. The burly fighter responded by imposing his own special conditions; as a means of protest, he permitted himself to fight using only a brass lamppost.

Pros

+ Nice 1v1 + A lot of Damage + Strong Late-Game

Cons

+ Squishy Early-Game + Needs strong items + In early-game, he has high Cooldown

How Beat Jax: Avoid attacking him when he turns on his Counter Strike. Try to do short trades against a Jax, as Jax excels in long extended trades because of his passive and ultimate. You want to win before 6, after 6 is where Jax gets most of his power.

Relentless Assault
Jax gains 4% - 14% (based on level) bonus attack speed for 2.5 seconds every time he lands a basic attack, stacking up to 6 times for a maximum of 24% - 84% (based on level) bonus attack speed.
This passive increases attack speed in percentage, so, build items with attack speed like Blade of the Ruined King or Guinsoo's Rageblade
Leap Strike
Jax dashes to the target unit or allied ward. If his target is an enemy, he deals physical damage to them.
Use this skill to chase your enemy or to escape, because you can use this skill in minions, allies and Wards.
Empower
Jax's next basic attack or Leap Strike within 10 seconds deals bonus magic damage.
This skill resets Jax basic attack. One nice combo is jump on the enemy, basic attack, and then W. Oh, and is very good with Trinity Force passive.
Counter Strike
Jax enters a defensive stance for up to 2 seconds, blocking all basic attacks and reducing area of effect abilities by 25% for the duration.At the end of the duration or if Counter Strike is activated again, Jax stuns all nearby enemies for 1 second and deals them physical damage, increased by 20% for each attack dodged, up to a maximum of 100%.
Jax´s utility skill, it´s good to clean waves, is one of the most important Jax´s skills and is very good in Team Fights. You have to know the perfect time to activate.
Grandmaster's Might
PASSIVE: Jax deals bonus magic damage on every third basic attack within 2.5 seconds.
ACTIVE: Jax gains bonus armor and magic resistance for 8 seconds.
Ooohh boy! This skill gives Jax one instrument of consistent survival and exceeds almost every 1v1 and have a long duration. Needless to say the passive is amazing and gives you more damage.

Boots

Your boots can be Mercury's Treads against strong AP or CC.

Ninja Tabi against strong AD like Fiora or Yasuo.

And Boots of Swiftness if you are want to catch your enemies.

Sustain

Blade of the Ruined King is more recommended against tanks and gives you life steal, and have slow to catch the carries.

On the other hand, Hextech Gunblade gives more sustain with life steal and spell vamp. Both have slow.

Stuff

Trinity Force offers everything, not only attributes, but versatility too. Your basic attacks gives slow and every attack following one skill gives bonus damage.

I really like Sterak´s Gage on Jax, prevents you to be exploded, giving one shield after receives a lot of damage. Can be substituted by Maw of Malmortius if you want more damage.

I recommend rush Guinsoo almost every single game, gives AP and AD, and the passive is... ooohhh... excellent for Jax. You don´t need to start with Guinsoo, but is very good.

Tank

This item gives more opportunities to arrive the ADC, and "disable" the enemy team with the active when you are in a TF.

Banshee's Veil is like Sterak's Gage, helps you don´t be destroyed by the AP carrie giving you a shield.

I could not talk about every item i recommend, because the guide would never end

You can do any type of runes for Jax.
He is Tank, Damage Source, AP, Life Steal...
Anyway, look the game, and see what your team needs.
But, i recommend this:
Or this:

Okay, im gonna show three options of skill sequence.

1)R>W>Q>E
Do this, if the lane phase is basically All Win, in other words, melees like you.

2)R>Q>W>E
This first one is for poke. Better if you rush Sheen as first item.

3)R>E>W>Q
Defensive option, with a huge Lane Clear.

When a TF starts, try to jump on the carries, burst then. If you can do that, you already do you work.

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Dont start a TF, this is for tanks.
Because of Jax´s E and Ult some people think he is immortal. Never starts a TF, unless you want to be destroyed.

Soon im gonna complete this guide.
Thanks to jhoijhoi's Making a Guide guide!
And of course... Thank You.
Remember to see my other guide Darius Ultimate Guide