Hi there and welcome to my first guide!

I'll try to explain in this guide how to flatten people with your leap strike to pummel them down afterwards.

This guide is for

Dominion!

To-do:
Pics about when to use empower.
Make the guide look nicer.
Finishing it.

Pros - You can 1v1 anyone! - You'll notice a lot of doubles and quadras if you're doing it right. - You have reliable hard cc, that's rare! - Great scaling!

SPACE

Cons - You'll rip your hair out if someone manages to get away. - Prone to ranged harass. - If you get cc'd, you're dead.

The runes are quite straightforward.

• Greater Mark of Attack Damage: Should be straightforward. Early game you're supposed to do lots of damage, combined with prospector's blade and masteries this will yield 32 extra AD, you'll start with 98 AD!
• Greater Seal of Vitality: I notice I lack hp late game, so how do you counter that? Seals of vitality. You'll have a lot more hp without building an actual hp item ( neglecting )! Post-Ult-Rework: Now these also give nice synergy with your ult.
• Greater Glyph of Scaling Ability Power: Lategame you should have some more AP. Scaling, otherwise you'll fall off. Since most of your skills scale of ap, this is a solid choice.
• Greater Quintessence of Ability Power: The amount of AP that these Quintessences give is an astonishing 15 AP! This doesn't sound much, but will add some nice damage to your q-w combo!

I don't consider other marks/glyphs/Seals viable. AD/l marks will hurt your earlygame damage, no HP/l makes you less tanky lategame and no AP/l hurts your lategame quite bad. Quintessences are different, feel free to experiment. I just consider these the best after quite some games with Jax.

Ah, the masteries.

You should open with a Prospector's Blade and a Boots.

• Prospector's Blade for the tankiness and early damage ( you won't notice lifesteal ).
• Boots for the movement speed, you need to be able to stick to your opponent. Also, your has a ******ed high cooldown.
• Health Potion depends on the player, I take it with me and pop one at a fight, it makes you last longer. I survived with 4 hp teemo's poison with these drinks!
• Phage, this makes you beefier, grants you a bit of extra damage and makes you stick to your targets better. This somewhat compensates for your ******ed high cd on
• Mercury's Threads Level 2 boots of course, you should kinda always buy these.
• Dagger, you need to abuse your Grandmaster's's passive. You'll start to dish out quite some damage by now.
• Sheen, o god I love this item. Leap Strike will do an amazing amount of damage now. In long teamfights you'll be able to proc this a lot with Empower.
• Trinity Force, this item has just perfect synergy with jax. Jax scales off literally everything this item has to offer. From Ap, to HP to Movement Speed...
• Vampiric Scepter, now fights tend to take longer and you'll need some sustain. Pick this up for a meager 450g.
• Hextech Revolver, spell vamp, now you'll gain hp from any kind of attack.
• Hextech Gunblade, no one can run, your hp will be restored after clearing a minion wave and let's not forget the nice damage it offers!

The game mostly ends here.

If it somehow manages to drag on for so long, get a Guinsoo's Rageblade. Afterwards you'll want to buy something that makes you beefier. A dominion game shouldn't drag on for so long. Get health, his ult grants you tons of armor and magic resist, now you need more hp.

Someone pointed out, teadrinker, it might be smarter to get guinsoo's rageblade after vampiric scepter. If you need some quick damage, feel free to take it earlier. This gives the same amount of POW as the Gunblade without the sustain and activate, but a lot cheaper.

You should open with all of your non-ultimate abilities. Master-At-Arms should be prioritized at all times.
Empower should be maxed at 9, the mana cost stays the same and the cooldown goes down. You need this at a low cd to spam sheen procs.
Leap Strike & Counter Strike depends. I max Counter Strike first for the defensive stats it offers. Leap Strike should be maxed last, your chasing power should be insane once you reach 9 ( almost ).

Surge & Ghost synergize so well with jax and eachother.
Surge Increases your attack speed and thus the amount of Phage and Master-At-Arms procs, resulting in a lot more dps.
Ghost Gives makes it a lot easier for you to chase and/or run.

Combine Surge with Ghost and it will result in a fatty slamming and walking at the speed of sound. See for yourself.

This one is pretty hard, I'll add in some pictures ASAP.
Let's say you're walking from the mid to bot and spot teemo farming there. How to beat the **** out of him?
Normal combo:

1. Press E when you're convinced you'll be close enough to teemo to stun him. Not too early that it will proc in flight, not too late that you can't press e after you landed on him.
2. Smartcast leap strike on him. Don't you dare to click on the ability. There will be a time that he slipped away because you missed the q. That sucks.
3. Auto-Attack once.
4. Immediately after the auto attack press w.
5. Teemo should be stunned by your Counter Strike.
6. Your Master-At-Arms procs and your Phage probably too.
7. Smack teemo to death. Win.

All-out combo

1. Press E when you're convinced you'll be close enough to teemo to stun him. Not too early that it will proc in flight, not too late that you can't press e after you landed on him.
2. Press R and activate Surge, use the corresponding hotkey.
3. Smartcast leap strike on him. Don't you dare to click on the ability. There will be a time that he slipped away because you missed the q. That sucks.
4. Auto-Attack once.
5. Immediatley after the auto attack press w. This is very hard since Surge increases your attack speed.
6. Teemo should be stunned by your Counter Strike.
7. Your Master-At-Arms procs and your Phage probably too.
8. Smack teemo to death. Win.

With deadly I mean like deadly, the opponent won't survive unless you get cc'd or he's a tank ( don't focus the tank... ).
Edit: You don't have to activate Grandmaster's Might now since it grants defensive stats now. Instead, activate it when you get in a long (team-)fight.

This actually counts for every 1v1.
Teemo Bait blind, immediatley pop e and whack him a couple times. You should win this trade and eventually be able to kill him. Rush phage.
Malzahar Pre-6 you should be on his face 24/7, easy kill lane. Post 6, when he starts spamming his spells in rapid succesion, immediatley press e. You'll stun him while he ults you.
Nidalee Pre-6 you should be able to win, try to go for the kill, harass won't work ( e + heal )
Karthus Iffy, if you manage to dodge most of his skills or he just plainly sucks, you should be able to kill him easily.
Ezreal Annoying gopher, bait his e and punish him twofold.
Udyr Don't, go top or something. Udyr is a beast. I wouldn't risk it, but in case you still go bot, ask for ganks and try not to get baited in using e.
Fiddlesticks Start with mercury threads, when he starts to drain, stun him.
Vladimir Lol? What is he doing here? EQW dead bloodsucker.
Shyvana Should be doable, not much to say. Try to dodge her twin bite, it hurts.
Katarina Pop e when she ults, pre-6 you shouldn't be able to kill her unless she shunpos to last hit a minion near you ( what good kata's will never do against a jax ).
Jax Wut? Bait his e, when he q's to you you q to a minion out of his stun range, pop e and try to stun him. This should be ridiculously hard.
Anivia Same as vlad. You get deadlier with each auto-attack, if she becomes an egg, you'll beat her to death in no time.
Shaco Sneaky bastard, if he becomes a huge threat, consider a hextech sweeper. I'm not a fan of it, but there are exceptions.
Vayne You're a hard counter to her. You know what to do.
Fiora ^
Warwick Ehh, try to not 1v1 him, he's the only other champ besides udyr who can stand toe to toe with the post-early game.
Fizz If he uses his Playful/Trickster immediately jump on him and trade with him. He shouldn't be able to trade with you.
Lux Dodge binding, squash her, win.
Cassiopeia Sit on her face pre-6, no hard cc or escape.
Kassadin ^, With the exception he can silence, slow and riftwalk. He can't dps though ( unless he goes dps, which you counter ).
Tristana Same as vayne.
Jarvan IV Never met one.

Based on my experience in Summoner's Rift and The Crystal Scar

Well, this was my first guide. Don't forget to post supportive comments and rate my guide. I'm ok with it if you thumb me down, but please, tell me why.

-Hixxar

> I think it's important to note that I don't play ranked, but I have:
355 Wins
290 Losses ( 55% win rate )
Normal games + Ranked and
44 Wins ( of like 30 with jax )
24 Losses
Dominion games ( 65% win rate ~2/3)

My guess would be that my dominion ELO is quite high, but to be honest, I've no idea.

Note: English isn't my native language, e-mail/text/whatever me major errors in grammar.

Thanks to jhoijhoi for the guide, dividers, etc.