Health 3301
Health Per 5 Sec 17
Mana 1215
Mana Per 5 Sec 14
Armor 104
Magic Resist 102
Attack Damage 246
Crit Chance 30%
Crit Damage 200%
Attack Range 125
Movement Speed 471
Ability Power 499
Attack Speed 81% (1,545 APS)
Life Steal 40%
Spell Vamp 50%
Armor Penetration 6
Magic Penetration 15%
Cooldown Reduction 3.0%
Dodge 36%
Gold Per 10 Sec 0
Reduced Death Time 0%

Hi, first of all I wanted to say English is not my native lenguague, I learned it through my years in Highschool and mostly playing games and watching movies and stuff like that. So, be aware, there will be spelling mistakes, grammar mistakes and sentences construction mistakes.

I decided to make a guide of Jax because he's one of my favorite champions, along with kass. Usually I do well with Jax, so I wanted to share my knowledge of him with you. So far, this is the most effective build I've played. (And it has had a lot of tweaks since I started playing The Granmaster) Note that all the Skill sequence and item purchase order should be used as a guide, but not strictly follow it, because you have to examine first the champions you are playing against, then the items they buy. I'll explain it further in the items section.

So, Jax is a great champ, mainly because he doesn't depend much on teammates,(for ganking)
and you feel like no one can solo against you. This is proven best if you mid, no champ you lane against will be a trouble until lvl 6. Malz would be a trouble lvl 6 if you dont play careful, or annie, etc. But before lvl 6 you can burst them hard with Q and W, E if minions attacked you, and ignite. If you feel you dont fear any champ 1vs1 then you are playing the Mighty Jax.

For Runes I take Magic Resist glyphs and dodge seals. I find the Magic resist runes very cost effective, and useful too. So I go with those. Dodge seals are a must for jax, you can go with armor seals too, but I strongly recommend dodge so you can hit E early much easier, when you have no boots.
The marks are AS runes. I've done some testings and with 25% AS, you can leap strike and autoatack once any enemy even if he is retreating. Havent tested against a janna team though. These marks allows you to charge the 3 hits you need to proc the additional magical dmg of Relentless Assault more quickly, and also charge the ulti faster.

I don't like the traditional 9 21 0 for Jax. Defense isn't my style. I go for a lot of dmg, buying doran sword first. As I use ignite I put one point on embers.

Ignite
I use ignite because it fits well with my Burst in out jax combo.

Flash
Is a must for me. I got so used to play with this that it is always fixed on F button. Its the best summoner spells for me. Many many uses. 1°Escape, especially if you flash out over a wall. 2° Reach someone to Q kill him. Go to the back of a teamfight, kill and injured squishy target, and the flash through the fight to my teammates, or flash through the enemy tank line and hit the squishy targets. (You have to escape faster afterwards)

Any spells you know how to use it properly can fill the spot of ignite, but please, please, keep using flash.

Playing Mid
Playing mid will allow you to harass calmly.
Okay, your harassment sequence is from lvl 1 hit with Q and then back. (Care if the enemy has a lvl 1 stun or snare as the enemy minions can depleat your hp, and you will end up more harassed than your enemy)
At lvl 2 is Q and just when Jax jumps hit W. You can also Q then wait for an autoattack and right after hit W for more effectiveness, but its just harder to do it because the enemy will fall back.
At lvl 3 you decide if lvling W or E. If he is an autoattack enemy, go for E, if he is a mage that only pops spells go with W. You might want to just harass him with Q until lvl 5, where you got the lvl 3 W (Empower) and surprise him dealing much more dmg he think you will do. This will allow you to have a more confident enemy, that maybe, will stay in the middle of mid with 60% hp, you can Q W him and then ignite them and hit E after dodging a minion attack. Or at lvl 6 stack your ulti two times hiting minions and then Q W your enemy and ignite.
In ranked games players are smarter, so I just harass them with Q and let them advance a little in lane. Then I leap strike him, W, ignite and force him to use flash, if he is someone with low hp he might die, and if not I make him waste a flash. He he dont flash, then I got a kill.
Again, all depends who are you laning against. I'm commonly refering to those champions you usually encounter mid.
I build shen early on for the main reason of making jax a burster, in ranked games you will find yourself 70% of the time in teambattles, and big ones. So you need to focus the high dmging champion and bring him down. Flash is your way out, or the stun from E, or good positioning will lead you to an easy run escape.
Jax can stay in battle longer, but only if they are small 2vs2, 1vs2 battles. And those are more common in normal games. So Shen and then lich bane makes him a burster.
Also when you have Hextech gunblade you have to use the active on the one you are bursting, your burst will make all your allies to focus on him seeing he lost a lot of hp and with the slow he wont be able to escape. So a quickly death makes a 5vs5 a 5vs4. Thats what you have to do. Teamfights are won focusing someone, and someone who has high dmg output and is almost unreachable (most of the times) because he stays at the back of the tank line. So you have to pass the line burst him all you can and then run away from the enemy team. This will cause your team to advance toward the bursted slowed squishy champion as the enemy team attempts to grab you since you are alone, and they will kill the squishy. After that you have to come back to your allies or they will kill you and the efforts will be for nothing. You can use flash if you didnt use it before, or Q to the last enemy or first ally or a ward and come back. If you have E ready you can hide in a brush wait them to come stun them and then go back to your team. Remember, wards are very useful. Put them correctly and you can escape easily. Always carry a ward with you in case you need it to go through a wall.
There is a moment in the item sequence where you have blidgewater active and hextech active. Remember to use them both. I reccomend using blidgewater right after landing with Q because it has a short range, and using hextech later so you guarantee maximum slow time, or using them both at the same time if you are bursting.

Playing top or bot lanes
Solo isnt very good. You are not ranged and harass you can cost a lot of hp. Ask your jungler to gank as fast as possible and meanwhile entertain yourself tower hugging.
Duo lane is easy as long as both enemies are autoattackers. If they are mages, you have trouble.
Even if one of them is, its very difficult for jax, you should have a ranged lane mate. Try moving between lanes to gank, and only engage 2vs2 in lane against mages if you are sure you can bring them down, and dont forget to hit R.

I like to start with Doran, it gives you more dmg, and its highly noticeable, dont know why, but you hit much harder. Then I buy the boots, then the hextech revolver, you can heal great amounts of hp in little time using Q and W and E and R third attack. You can go for blidgewater too, but i recommend hextech, cuz its more like "healing burst", blidgewater is more like a continual healing, but in lesser ammounts.
Shen will contribute to your burst, and also let you jungle much easier. Dont forget to get red whenever you can, even without shen, you can do it up from lvl 6.

Hextech Gunblade x2
This is a great item, gives more AP more AD and lifesteal and spell vamp, also having a neat slow.


Phantom Dancer
This item is one of the best because of the movement speed, highly needed to gank and escape. Also has more AS and crit chance.

Lich bane and Rabaddon
Lich bane will proc with a lot of extra dmg from ap gained with the two hextechs plus embers plus rabaddon. Your burst willbe awesome, also the turrets will go down quickly as hell. At this moment you will be able to backdoor any tower you want. And destroy them in fact in 6 seconds

Another option is go for infinity edge and/or the bloodthirster, you'll decide that depending on the enemy team composition and items.

*Be smart, dont follow the item sequence to the letter: if there is another jax, or teemo, etc buy Sword of the Divine, tell your friends not to attack jax so they dont give him E, activate SotD and bring jax down, or teemo if he blinds you.
*Also we aware if an enemy buys SotD, try to stay away, or aproach so he activates and then leave until the effect is finished, unless you know you can defeat him of course, try to dodge before engaging him, so you have E ready.
*If someone is recovering health like fiddle leash or yi's meditation hit them quickly with ignite.
Buy oracle quickly if there is a teemo and destroy its shrooms. Very important, because shrooms reveal your position, on top of slowing you down.
*If there is a mage burster that depends on his her combo, buy banshees. Example: Leblanc, he will be forced to chain you first or wait to someone took it from you. Also remember pressing R before encountering her.
*Dont wait until you have 100 hp to drink a potion, your health must be always full, so that discourage your enemies to attack you, they will attack instead your mate if he is lower than you.
*Dont wait until the last moment to use flash, use it before the enemies uses their abilities, because it might be to late if not. Also a quickly good used flash when full hp discourage your enemies of following you.
*During teamfights avoid being focused, this is acomplished by skirmishing, going in and out, maybe you can initiate, but quickly flash or Q out so your enemies will still try to attack you for a brief moment, but during that moment they will be punished by your teammates. Right afterwards they will focus your team members, but with their hp reduced. After everyone has his target you get in again aiming for the squishy.
*Note that jax skin "vandal jax" is the less noticeable during teamfights in summoner rift, and perhaps also in twisted treeline. (summer version) So its easier to get less focused on teamfights.
*Try not buying the 3 pots (blue red and green) as it makes a super shiny white aura that makes you a lot more targeted.
* Build this way you will have a lot of both damage, magic and physical when lich procs, but we catious engaging tanks and overextend persuing them.
* I've learned that if you play safe, if your entire team can play safe the other team will start to yield dispair (hope thats the correctly expression) and do risky things such as extremely towerdiving. If you and your team manage the situation well, you can get away with it, and have a clear advantage for the rest of the game. This strategy is easier to appy if you are with friends.