I'm ValeCallampaXD. I played my first league game with Xin Zhao. It was such a fun and easy champion to play. I remember just jumpin in and killing everything.
After xin stopped being a free to play champion, i really didnt wanted to play any other, but i havent enough ip to buy it.
So I asked a friend: "is there any champion like Xin Zhao?". His answer was simple and clear: "there is no champ like xin zhao, but there is someone better; Jax"

Jax has an incredible lvl 1-3 combat thanks to Counter Strike. Even though he has no pushing nor ranged abilities, you just need to jump to a champion to kill it almost instantly.
Jax's weakness is in levels 4-9 or so, but you will own anybody at levels 1-3 and will own an entire team on your own at 18.

Pros
+ Offers the best combat at lvl 1 due to his Counter Strike: perfect for invades
+ Will own anybody at lvl 18
+ OMG! THE DAMAGE OF THAT Empower! STAWP! MY FACEE!!
+ Incredible burst and dps
+ Really tanky without Grandmaster-At-Arms
+ Inmortal with Grandmaster-At-Arms
+ You jump on someone: you've killed someone
+ Great and easy minion farming
+ Low cd on ult (and all his abilities exept for Counter Strike)
+ Spells have low mana costs
+ Really good at escaping from ganks




Cons
- Easy to learn, but hard to master
- For noobs at jax is really hard to use Counter Strike
- Bad sustain in lane
- Pretty bad against pushers
- Aginst what a lot may think, jax isnt a good iniciator for teamfights

At the moment of leashing blue for your junler, make sure the golem attacks you and use dodge. Your team will have 3 seconds to freely attack the golem recieving 0 damage. Once dodge and the stun are over you can make the golem hit someone else, know that you did enough.

Jax shines at low levels (1-3). When you have Counter Strike, Leap Strike and Empower at lvl 1 each, you are the strongest champion on the map. Anybody you jump to (unless its a Singed, Yorick or Jayce) will be dead.
Anyway, you are really weak against ranged champions like Teemo or agaisnt champs with ranged abilities like Pantheon. Farming minions with Jax can be a real headache against this type of champ so be sure to harrass him.

IMPORTANT TO READ!!
How to harass soon game with jax?
Leap Strike to him. In the air, use the Counter Strike to start spining your lamp. When landing, check if the other champ is running away or will fight you. In case it decides to fight, let the dodge continue working. If it runs away, press e as fast as you can in order to stun him in place.
After this, basic attack him and quickly press w and attack him again.

Now, if you think you can kill him, do it. Remember to use Exhaust and Ghost to make your kill secure as a kill soon game is amazing to any champ.

If you cant kill him and you are afraid of a gank or that he can deal more damage than you, just walk away and continue last hitting. With the combo listed above he will have 50% of his life, and he will think twice before coming close to you again.

YOU CANT LANE PASSIVELY WITH JAX, BE AGGRESIVE!

This is possibly the only weakness of jax. Mid game for jax is considered after being lvl 4 and before having trinity force.
Without trinity force jax is pretty weak, but once you've build it you'll turn into a killing machine (and the effect will be doblued when you archieve to have hextech gunblade)

My biggest tip is to ask for several jungler ganks and never stop farming.

GET THAT TRINITY FORCE AT ALL COSTS!

IMPORTANT TO READ!

Dont think that because of dodge you are a good iniciator for teamfights. Jax isnt good at that.
Let your malphite, amumu, alistar, or sejuani to do that. Once that is done, jump second, right after your tank and activate your ult. DONT USE DODGE YET! as soon as you recieve 100 damage, activate your dodge. In the middle of the teamfight, the enemy adc wont see that you are with your dodge active, so he wont realize his basic attacks are dealing 0, 0, 0, 0, instead of crit 890, 350, crit 886, crit 900.

As soon as you have your q again, jump to the enemy adc and use the active from hextech gunblade on him. SECURE KILL.
Be careful when your ult is off. Once grandmaster's might is on cooldown you arent considered a tank anymore and your surviving posibilities are poor compared to before. Make sure to spam your w every time you can as it has really low cd and thanks to hextech gunblade you will recieve a lot of hp back from the 20% spellvamp and the lifesteal.

Roam in the jungle with no fear. Jax can virtually win any 1v1 without any troblue late game thanks to trinity force, hextech gunblade and guinsoos regablade (at least is a cho gath you are fighting against :C)

PUSH LANES!
With guinsoos regablade, relentless assault and grandmaster's might passive you will push lanes and kill towers like a boss

HARD LANES


Yorick is the hardest lane for jax. Jax is strong because of his e blocking basic attacks. ¿How do you want jax to do something when you are against a champion that his damage doenst relies on basic attacks? HARD!



Singed is the most b*** lane you will have to fight. You can't dodge his poison, and he is so fast that you simply cant perform basic attacks. He will Fling you as he wishes. YOU WILL BE HIS PUPPET!
Ask for constant ganks. Singed will be in a real hard time if your jungler has long cc, like sejuani or amumu. (not with hecarim or nocturne)



Jayce will push you a lot, and when you jump on him, his e and q can burst you out more than you can burst down him. HARD



Cho gath, before level 6 is really an EASY lane, but one he gets lvl 6.... it will be the most frustrating lane in your life. There will be nothing you can do against him, he will tower dive as he wishes, burst you down like no other champ can with his Feast. Apart from this, lvl 6-7 is considered mid game, and this is the weakest moment of jax. THIS WILL BE YOUR HARDEST LANE EVER. Kill him as much as you can in low levels so you can survive lvl 6.



Renekton is also a really hard lane. He attacks more than you, he stuns for more time than you, he has a lot of sustain, he is more tanky than you and his ult is even better at defending. Ask ganks from your jungler. This is renekton biggest weakness.

EASY LANES


Fiora..... what to say. He does 0 damage to you as all his spells are upgraded basic attacks (you dodge them all). You can even dodge his ult! If she uses ult and you have your dodge on, you will see MISS, MISS, MISS, MISS and recieve 0 damage. EASY LANE



Vi its also an easy match up. Vi depends on the shield provided by her passive to do something in lane. You put that shield down with one basic attack, and then press w for a good placed empower and begin to consume her life.



Xin zhao its another easy lane. As any other basic attack based champion, you can dodge most of his attacks.



Aatrox will also be easy. Aatrox relies on his life steal to be the **** he is. He can't get hp from basic attacks that attack 0. EASY. But watch out! He will eat you when you don't have your dodge! dont waste it!



Irelia will also be an easy match up as you can dodge that awfull true damge that makes irelia so op.



You will own any ad master yi or tryndamere that goes in your way for a logic reason. GIFTED MATCH UPS



You will also own all those people that insinst using adc's like caitlyn or kog maw top.