Do you guys remember those AD guides long time ago and then everybody just decided to go for the hybrid AP which i find useless at lvl 18. I have played many many games with jax and even though i am lvl 27 i have probably played between 200 and 300 games with jax. I have played with him 3vs and 5vs5 and i have been able to take all lanes, even solo in summoners rift. All you need to know is how to manipulate the guide for each lane and to who you are versing.

The Glyph: I recommend Greater Glyph of Ability Power so your abilities do more damage at the begging of the game. You can replace this if you like with either Greater Glyph of Magic Resist or Greater Glyph of Cooldown Reduction . The greater Glyph of warding is better if you expect to be laning against a mage. And the cooldown reduction Glyph is better for spamming your abilities.

The Mark: For The marks you have a choice between 3 different runes depending on your playing style. I recommend Greater Mark of Desolation above the rest but alternatively you could use Greater Mark of Attack Damage and use this with your masteries to have an edge when lvl 1. Another choice you have of the marks is to use Greater Mark of Magic Penetration which would be better if you want to go for a more AP build. Also don't be afraid to mix and match here.

The Seal: OK you only have one choice for seals which is Greater Seal of Evasion , come try to argue with me you will be shot down by every single person who as ever played with Jax.

The Quintessence: At the moment i use Greater Quintessence of Ability Power but this is cause the only other set of Quintessence's that I own are damage Quintessence's Which you only recieve 2.25 attack damage per Quintessence and the AP Quintessence gives you 5 ap per Quintessence. I have seen other people buy Greater Quintessence of Evasion which is another choose but i have not yet tried this.

But remember for whatever runes you choose to use make sure you match it with your mastery page to have the edge over your opponent/s at lvl 1.

All you need to know is how to match your runes with your mastery page. I will mention a few core masteries you should unlock:
Firstly: Arcane Knowledge : all your abilities produce magic damage dont they?
Secondly: Weapon Expertise : so when your abilities are on cool down you can PIERCE THAT ARMOUR!!!
next should i choose Vampirism or Blast by far Vampirism !!! Why would you choose blast when you are doing attack damage end game and vampirism lets you lane longer and if you choose Doran's Blade your lifesteal will actually do something.
Sunder would be also be a good choose for even more amour penetration.

One of the first things you should get is Summoner's Wrath but only if you choose Ignite , Exhaust , Ghost or Surge, but i recomend using Ignite and Exhaust .
If you choose Ignite and Clarity then i recomend you also get Summoner's Insight as a mastery.

Executioner is unnecessary but is useful for killing people under 40% health.

I always max out Brute Force and Mental Force because of Jax's passive so this is benefiting Jax in all ways.

IF you can try and max out : Hardiness and Resistance which will benefit you while laning.

I specialize in soloing in Twisted Treeline which i have played about 150+ games with Jax. You can either start with Vampiric Scepter or with Doran's Shield, i prefer theese two items because You can lane longer with jax and you arnt forced to go back so early with happens often if you choose Doran's Ring or Dorans Blade . One advantage i find is to go to the top lane earlier than the other team, YA go help with first blood but make sure u get a head-start in lvls because jax most important ability is counter strike. So soon as you are lvl 2 always upgrade counter strike. Most of the time i find that it is difficult to kill people while you are under lvl 6 but it is still possible. Normaly i would empower and hit them but then all the minions will target you which helps in your favour cause that means that you will eventually dodge so u can stun him but if you dont get a dodge then a mix off all the minions and the other player will be damaging you and if the other player iniciates a fight then stay by your minions if you are a low lvl cause the minions will do alot of damage to him maybe even more than you. When comboing your abilities you will find that you will loose mana very quickly and the only way to stay your lane is to use your abilities at the lower lvls that is why i recomend AP at lower lvls and AD at higher lvls.
If you end up killing your opponent and you have enough for Ninja Tabi then i recomend you go back quick as possible unless you are almost lvl 6 then get to lvl 6 and fetch the boots, At this point you should be invincible against 1 person, do not try and gank two other people you will die because you dont have any spell vamp or lifesteal. The next thing you should buy is a Hextech Revolver and soon as you get this go do drag which you should have no problem with, I normaly do drag at lvl 8-10 which is quite early, if you are lvl 8 you might need a friend to help but make sure no one see's you otherwise they might gank you while taking drag.
Next thing to do is finish your Hextech Gunblade which will give you everything you need for jax. After that buy a Guinsoo's Rageblade , this item fits jax perfectly cause of its passive which mixes with your ulti's passive and the ability power it gives you and the damage. After this everybodies guides very, I prefer to go AD. Have you ever seen a jax do 40% of your health at lvl 18 when he jumped and use empower on you, I though not, and after that he does constant crits on you of about 600-1000. This is why i prefer AD to AP. I normaly buy another Bloodthirster instead of a Infinity Edge and a Black Cleaver instead of Atma's Impaler but it all depends on who you are versing. You cannot beat a AD jax at lvl 18 only reason you have AP is for low lvl fighting when you are using your abilities often. I forgot to add that with those constant 600-1000 crits you also have between 1.8-2.4 attack speed after a while plus a aoe stun, THAT IS WHY JAX IS OP!!!

Will do this guide tommorow But for now i will give you one tip: if you are attempting to go mid with jax which is possible make sure you have plenty magic ressist. and i would buy Doran's Shield for it's health regen which you will need while waiting for your abilities to cool down because you wont be able to harras your oppenent with your normal attacks but a mix of your jump, empower and your stun you should be able to kill your opponent.

I will do this later along with summoners spells, summary and when i get to lvl 30 ranked play. I will try and finish Summoners Rift tommorow