Just updated this guide as of April 18th 2012 with updates in the match up, mastery, runes, and items sections.

Jax is an extremely powerful duelist who can take almost (I'll explain why I said "almost" later) every champion in a 1v1 battle. Jax excels most as a solo top champ due to him being amazing in 1v1 fights but he can also jungle quite effectively if played right.

This guide will give an explanation of skills, masteries, items, and strategies against solo top champs after the Jax change. Currently Jax's dodge has been "nerfed" per se, but, even though he doesn't dodge every attack, he now has a reliable stun. There was the initial change, then an update as well.

Marks:
Greater Mark of Attack Damage - I get flat AD runes here to help with early game damage and last hitting.

Other choices:
greater mark of desolation - You could also take flat armor pen runes, but since his Q (leap strike) scales so well with AD I prefer AD runes.

Greater Mark of Magic Penetration - These work because a good amount of his damage does come from ablity power sources, but still weaker to flat AD runes.

Seals:
Greater Seal of Armor - For yellows you're going to want only the flat armor runes because you will need to negate as much physical damage early game as possible. Strong early game champs such as Gangplank and Wukong will go right through you if you do not have these runes, there's really no other choice.

Glyphs:
Greater Glyph of Scaling Magic Resist You are gonna want these in for some more late game tankyness. You wont need any more damage late game since you will be building glass cannon, so you will get some tankyess out of these runes.

Quints:
Greater Quintessence of Attack Damage Flat AD helps with last hitting and trading early since that is Jax's weak spot.

Now that Jax is able to build glass cannon again, you will want defensive masteries to survive in lane and in team fights. Once again, you do not need more damage because of your build.

9/21/0 Is your best bet for success. You could go full offensive but you would like survivability. If you do go 21 in offense make sure to grab 9 in defense getting the extra health.

Core: Just updated this as of April 18th 2012.

Against AD
If you are going to lane against an AD such as Gangplank or Garen, I would suggest starting with Cloth Armor to negate their early game damage and 5 Health Potion for increased sustain. You would then build this into Ninja Tabi as quick as possible.


Against AP
If you are going to lane against an AP heavy champ such as Rumble or Mordekaiser I would suggest getting Boots to help dodge their abilities and 3 Health Potion for increased sustain. You would then build these into Mercury's Treads.



First trip back:
For your first trip back,
Against AD: You are going to want to grab your Ninja Tabi and 2 Doran's Blade and a sight ward. You want the Dorans for that extra health when you start dueling since you should be around level 6 now.

Against AP: You will want to grab 2 Doran's Blade just like against AD and Mercury's Treads and maybe a sight ward.

Starting your build:
After you have your Doran's Blade you will want to start building your Hextech Gunblade as fast as you can starting with the Bilgewater Cutlass. This gives you great sustain as well as a great slow and some extra burst.

Finish your gunblade and start working on your Guinsoo's Rageblade starting with Blasting Wand against an AP lane or a Pickaxe against an AD lane.


Now you can go a few ways here.
If you are up against AD heavy or a fed AD grab Atma's Impaler or if it's pretty balanced grab a sheen. Now you wanna start building some defense.

Getting a Guardian Angel works wonders if they wanna focus you down or if it's a balanced team.

Heavy AD and they are focusing you? No problem Thornmail

They got a sustained damage AP like Ahri? No problem Force of Nature

They have a fed AP nuke like Viegar? No problem Banshee's Veil

UPDATE: I changed from maxing Leap Strike first to Empower. I would still grab Leap Strike first to avoid level 2 ganks and of course grab Counter Strike at level 3.

You will want to check out the "Tricks Section" for tricks on using his abilities than will help you significantly.



Leap Strike Q: Leap Strike
Explanation:
This is going to be your escape and chase tool. You can leap to enemies, teammates, friendly or non-friendly minions, friendly wards, Teemo mushrooms, Heimerdinger turrets. So pretty much everything. You wanna max this out first for the increased mobility via reduced cool down, and the damage is pretty good as well.


Empower W: Empower

Explanation:
This is your main controlled damage source, this is what you are going to want to use every time it's up. Max this second.


Counter Strike E: Counter Strike

Explanation:
This is Jax's big defensive ablity/cc. This is what you are going to use to either negate incoming damage, or to get a clutch stun off.


Master-At-Arms R: Gandmaster's Might

Explanation
This is basically a steroid for an ultimate. Since it lasts 8 seconds you are going to want to use this at the beginning of the fight because rarely will a fight last longer than 8 seconds.

Teleport If you are going solo top Teleport is a must.

Flash You will definitely want this for escaping jungler ganks. Flash is insanely effective if used before or right after a Leap Strike to a minion. If you are by the enemy turret and you flash to about mid lane, they still have a shot at getting you, but then you can leap strike away without a scratch.

Ignite This isn't a bad spell on Jax, but only grab it if you are facing Volibear or Dr. Mundo. It's strong against both Mundo and Voli because it will negate their heals. SO if you do grab it, replace Flash with Ignite. You are going to want to keep Teleport.

Exhaust This is just ehh. Wouldn't recommend taking it over Flash, Ignite, Teleport.

These are the only viable spells to take top, do not even consider any other ones.

Early game Jax is awful. He is extremely weak and will lose a lot of toe to toe battles with almost every champ up top. Levels 1-6 you need to just focus on farming minions as best you can to make sure that at level 6 you have enough money for your first trip back items. Since you do not have wards yet, and you are not going back until level 6, do not over extend too far.

Even though you have Flash and Leap Strike you do not want to get caught by the jungler because they could still easily kill you, or weaken you enough to where you have to recall without enough money for your items.

Once you hit level 6 you are going to want to harass often and hard. Jax is amazingly strong at level 6 due to Master-At-Arms passive. The idea here is that you melee a minion twice because ( Master-At-Arms passive activates on the third hit) then leap to your target, auto attack, then use Empower. This will do a good portion of damage and you can do it over and over.

Essentially once you hit level 6, you should have the lane won.

Since Jax is mainly a solo top champ, I will give a list of match ups of potential opponents you will face.

This is on a scale of 1-5, 1 being the easiest and 5 being the hardest.

Akali 3 - Well Matched
The only reason I gave Akali a 3 instead of a 2 is because a good Akali is hard to kill if they use her invisibility correct. She has pretty good harass, but at level 6 she can't touch you at all. If it's before level 6, and she uses her invisibility, try to stay back because her harass can hurt if you let her repeat it.

Blitzcrank 2 - Easy
Blitz can't do too much to hurt you, and even early game you should be able to take him down. If Jax beats you early game, then come level 6, you have no shot at winning. Just stay behind minions when farming to avoid his pull. When he is by his turret, stay in the bushes because one pull > knock up > silence on his turret and you are dead.

Cho'Gath 4 - Disadvantage
I gave Cho a difficulty of 4 because he is extremely hard to kill between his silence and knock up, and it's near impossible to tower dive him. Once you both hit level 6 you can hit him hard, but you gotta do it fast before you starts using his ult to beef up.

Dr. Mundo 4 - Disadvantage
When Mundo has his ult, he is nearly impossible to kill even for Jax. Although if you take Ignite instead of Flash you could land kills pretty easy if you ignite his ult. He can kill you early game though, so be careful and don't under estimate his damage.

Fiddlesticks 2 - Easy
Fiddle is a great 1v1 champ, and will destroy you early game with his drain/fear/silence combo, but once you hit level 6, he is just too squishy too survive.

Galio 2 - Easy
Galio can't do much to you, and he will usually stack magic resistance, but you can still box him out and farm really easy. Although you might not land a kill on him.

Gangplank - 3 Well Matched
The only reason Gangplank is a 3 is because is early game is nasty against you. You could grab a Doran's Shield against him to stop his pistol damage. He will hurt a lot early game and a good Gangplank will shut down your farm which could make it difficult.

Garen - 5 Major Disadvantage
Garen is really rough because he is extremely hard to kill and you can harass him all you want, but his passive will keep him at a good amount of health. His silence + spin combo will hurt, but you can leap strike away, unfortunately though you will still eat a good but of it because of his silence.

Irelia - 1 Easy
Irelia doesn't have much she can do to you, even early game. Early game she still beats you, but probably wont kill you. At level 6, you should dominate her

Jarvan IV - 5 Major Disadvantage
Just like Garen, he should be able to kill you, and you shouldn't be able to kill him. He has an excellent get away, and a good ult for trapping you. He's just too tanky with a good escape to be able to kill him.

Katarina - 2 Easy
Pretty good harass early game, but can't do much to you. She can jump to you instantly, but that means she does half of your work for you, saving Leap Strike for when she tries to run. Just Leap Strike away when she uses ult.

Malphite - 2 Easy
He doesn't do as much damage as some of the other solo top tanks, so you should have good farm, and you might even be able to land a kill or 2 on him.

Mordekaiser - 4 Disadvantage
Morde is really strong early game and a good Morde will keep his shield up to stop your harass, even at level 6. You could go toe to toe with him at level 6, but it wont be as easy as some other champs. Be really careful for his harass early game. Stay away fro your minions.

Nasus - 5 Major Disadvantage
Nasus might be one of the very few Jax can't go toe to toe with because if you both use your ult, he wins. Wither is gonna hurt your escape but Leap Strike should be able to handle it. Try to harass as much as you can at level 6 without starting a toe to toe fight. This will hopefully slow his farm.

Nidalee - 2 Easy
The only reason I didn't give Nidalee a 1 is because if she goes AP, 1 shot from her spear can really wreck you. Be sure to dodge spears and even Leap Strike if you need to avoid them. You should be able to destroy her though early game if she is AP. If she is AD, she can't really hurt you until level 6. Even then, you still win.

Olaf - 3 Well Matched
Olaf could very easily be a 4 but I think Jax and Olaf are pretty well matched. His Reckless Swing will hurt even with armor due to its true damage. When he gets low, he will destroy you as well. Save your dodge for when he gets low to avoid his massive damage increase.

Pantheon - 1 Easy
Wait, what does he do again exactly?

Poppy - 3 Well Matched
Poppy is pretty strong and her passive is a pain, but her ult isn't a huge factor against you. As long as you stay away from the walls, you should be fine.

Renekton - 4 Disadvantage
Rene has a good gap closer, escape, and a stun which makes for a pain in the ***. Just like Nasus, when he pops his ult, you can't win, so rarely will you kill him, while on the other hand, he can kill you pretty easily.

Riven - 3 Well Matched
Riven has a good escape, gap closer, and a stun like Rene, but also a minor shield. Since her ult doesn't make her invincible, you can kill her, but it wont be easy. Be careful if your low because she can ult a pretty good distance.

Rumble - 3 Well Matched
Rumble will tear you up early game and probably stop your farm, but you will shut him down after that. Since you wont be farmed though, you wont be as strong as normal.

Ryze - 4 Disadvantage
Ryze is really tough to kill because of his Rune Prison, but he is very squishy if you can get to him. Be careful though if you're low because one Rune Prison into two Overload, you will be dead.

Shen - 5 Major Disadvantage
With his new buff, it's a case where he can harass you early and hard. Not to mention he can kill you but you can't kill him.

Shyvana - 3 Well Matched
Shyv can't do much to you until she is level 6, but at the same time neither can you. At level 6 though the toe to toe fight can go in either direction, so be careful here.

Singed - 5 Major Disadvantage
Singed is one of the best tanks and the inability to chase I'm down makes it difficult to land a kill, and he can limit your farm pretty easily. Another case of he can kill you but you can't kill him, except he can kill you easier than some of the others.

Sion - 5 Major Disadvantage
He is everything Jax is not. Better stun, better ult, better harass. You will not be able to harass him, stop him from farming, or go toe to toe with him.

Talon - 2 Easy
Talon can't do TOO much that can hurt you, but is really effective at getting away. He wont beeat you, but you might not beat him.

Tryndamere - 3 Well Matched
Early game you are both pretty equal, but at level 6 you have the advantage. As long as you don't engage him when he has full fury, you could easily make him burn his ult. You might not ever kill him though.

Volibear - 5 Major Disadvantage
Voli does absurd amounts of damage for a tank and you will not kill him. If you took Ignite you might be able to land a kill but it's a long shot, kinda like Dr. Mundo.

Yorick - 3 Well Matched
Yorick has amazing harass and amazing life steal, so you wont do much to him even with your harass early game. At level 6 however, you should hit him hard, though you might not kill him.

This is one of the biggest parts to playing any lane. You want to always have 1-2 wards with you. So when you go back plan accordingly so that you always have 1-2 in your inventory as well as one already placed. Also, always make sure to check how much time is left on your ward. Otherwise you might over extend and realize your ward ran out as you fall victim to a gank. In case you don't know, you can check how much time is left on a ward by clicking on it and looking at the number on the white bar.

When warding you want to place it in such a way that you can see them coming from far away, but also close enough to see if they come out of their jungle. Most people will place the ward in the bush, or even at the end of the bush. This is alright, but it does not give as much of a warning that a ward placed farther out would. It may not seem like a big deal but 2-3 seconds of reaction time will make a break a gank.

Here are 2 examples of placing wards. The first one is wrong, the second one is correct.

WRONG ward placement



As you can see, that area does not provide as much reaction time as the second picture. Also, you see I have marked off the "tri-bush" area, keep away from warding that bush at all.




CORRECT ward placement



This is the correct area to place a ward. It gives you plenty of time if they come from the river, and it also shows if they come out of their jungle.

If you are being chases and have wards with you, you can throw down a ward over a wall, then Leap Strike to it for a clean, fast escape.

Empower resets your auto attack timer, so try not to use it until after an auto attack for a quick 3 attack combo. This may not seem big, but if you use it 2-3 times in a fight, that's 3 auto attacks right there, and that can really add up.

Counter Strike is now able to be set off after 1 second of using it. So what you can do with this is activate it, wait a second, then Leap Strike in and hit E again for the stun. Only use it in this way if you need the stun to set up a gank, or if you will land a kill by using the stun this way.

Another tip for using Counter Strike is to not use it at the beginning of the fight, or don't initiate with it, because after you use it, you have no damage mitigation. Use it after you see your health starting to fall. The idea here is, when you start to get lower, your enemy will want to keep attacking you to finish you off, but when you use Counter Strike you will stop their damage. By this time your passive and Guinsoo's Rageblade should be at full stacks or almost full stacks giving the the win in your 1v1 battle.

Using Flash when paired with Leap Strike makes for insane gap closing, so don't under estimate that combo if you are chasing and you think they are out of range.