Jax is THE most op Champ in the game, if you play him right. Sadly many don't making him the joke of the round. Here is the master way to play him, all items buff Jax abilities and therefor are essential for playing Jax right. If you get less than 20 kills in a round with this build you suck hard time and shouldn’t play LoL...

This is JAx passive ability gaining 3.5-11% Attack speed with EVERY STRIKE! This means the more health an enemy has the fast Jax will strike over time, in combination with Guinsoo's Rageblade making Jax absolute deadly

This is on one side an hunt down and Strike skill dealing both AP Dmg( 60%)and Attack Dmg (100%) + 70/110/150/190/230 to the enemy after the jump a moderate distance And also it is an evasive skill helping you escape enemies through jumping. A key element of this jump is that during the jump Jax doesn't get dmg, rendering some ultis or attacks useless when jumped right!

This is Jax golden ability along side his passive: even though the dmg of 40/75/110/145/180 +(60% AP) seems rather moderate compared to Leap Strike, the Cool-down is 1/2 of Leap Strike letting you smack it out every second at the end with Trinity Force. Above that, the Sheen build in of Trinity Force doubles your dmg after every use and a crit TRIPPLES it! In late game it has often happened that Jax is able to kill an enemy with one combo rotation alone (see bot for combo explanation)

No its no olt ego-shooter build into LoL. It is a Shield as it also is a Stun ability at the same time. It is awsome for evasion or even tower-dives, it blocks all basic attacks coming from Minions, Champs, Creeps, or even Towers for 2 seconds. Even though the ability does 100% increased dmg for every attack dodged, no Jax i know waits that long. with a second activation Jax can end the ability resulting in a 1 sec stun of the enemy minions and foes

The hidden passive of Jax. After every 3. Strike Jax next strike is increase by 100/160/200 (+70% AP). This of course stacks with Empower, the Sheen and a Crit. Further more, by activating this ability 30/50/70 +50% Attack power and 30/50/70 +20% Ability- Power AND Jax armor are converted to Magic resistance. The most magic resistance a Champ can gain without Items

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It is important to activate Counter Strike right before Leap Strike so that the enemy has no time to react. After the enemy is stunned smack him over and over with Auto attack and Empower. When the enemy starts running, just repeat the rotation.

The Items are the bread and butter in every round. Especially if they support the buffs the champ gets through his abilities.

Always underrated especially due to the fact, that 12% dmg can become a whole lot of dmg blocked in late game. The armor is a wonderful add for Counter Strike and Master-At-Arms

Gives you just the right dmg boost, slow and Hp, to win your first 1 on 1s in the early game and of course are part of Trinity Force

Come on, do I realy have to explain why?! Attack Dmg, Attack Speed, Cool-down reduction, Health ,Mana, Movement speed AND a build in Sheen in one single item?! COME ON! The Phage buffes your Empower and helps you hunt, the Sheen doubles your auto hit dmg after every ability use, and Stinger stacks with your passive Relentless Assault. Its a MUST HAVE.

Remember that this build is constructed to do Massive DPS and this item turns them in to Health for you AND provides AP and AD for your Master-At-Arms. The key why this Jax build survives every single gank (if not stun spammed of course)

Gives AP, AD and Attack speed, and it has almost the same Passive as Jax own stacking the speed even more and faster. The effect will be MASSIVE DMG, due to the fact that you will faster hit a crit that deals up to 300% Dmg (if crit stacks with Empower and Sheen. This item can let you one hit enemies in ganks, drastically decimating the enemies inside the gank. Sum: The faster and the more you hit the likelier it becomes that a crit is amongst them and crits can really hurt when dealt with a Jax

There isn’t actually much more to say with Jax since I never go out of a game with less than 20 Kills, and hes the only char I ever won a 2 vs 5 game with. Against magic attacks your Counter Strike will shield you most of the time, if not for instance vs a old Ryze, Veigar or Kennen, simply add your Ulti. Watch out that you don't get too greedy or too cunning with him throughout the game letting you foolishly get killed (this often happens to me, cause its fun to tower-dive with Jax getting another 2 kills or trying to get 3 kills at once, or trying to do Nasher alone, which doesn’t work anymore :( (unless you get the full build at the top, just keep stunning him^^)
Fiora, Yasuo can be pesky but remember: if shes stunned YOUR doing the dmg and a huge amount of it!
Illaoi is all muscle and no brains. When you get caught in her Ulti Counter Strike her and Empower her to her knees.

Ou yea and one last tip: Jax never retreats! Either you will be leading the fight or you will Counter Strike the enemy so your team can run to safety. Its a Team game and Jax gets more then enough kills as it is.

The Guide is not finished yet but these first impressions should get you going. Have fun and Smack 'em down!