Hello, I'm Nalex (Aka Axo). I'll shortly introduce myself:
I'm a casual gamer, I play FPS-games, MMORPGs and MOBAs.
I've been playing League of Legends since "pre"-season 1, started on the NA-servers, jumped to EUNE when Europe got servers and EUNE is my main server for now. I do have an account on EUW.I'm just an avarage player, I usually have fun playing and most of the games I do well (atleast I like to think). So this the first build I'm doing, planning on doing builds/guides on other champions that I like.
Hope it will will help somebody else too! Enjoy (if you can) :)
By the way, as this is my first guide I'm making, I would appriciate comments and toughts about what I should improve, waht is good and what's bad (or more negative).
I'm aware that I haven't made a detailed Jax guide (Combos, how to succeed etc.), and it will come in the near future! I'd like some feedback about the overall guide, both looks and contents.
NOTE that the more advanced guide will pop up here asap, I just need to plan it a bit.

Pros/

• Manly
• Strong (if played right)
• Tanky
• AoE stun
• Hugh burst and sustained damage

Cons/

• Not very strong at levels 1-3
• Scales off in hyper-late game
• No Tryndamere Ultimate nor Teemo passive
• I think that was all.

Masteries:
Pretty standar setup, I chose to do 19-11-0 but you can really do wahtever fits you. If you want to be a bit tankier 9-21-0 will do just as fine. I don't have a lot to say, pretty self explanatory.

Runes: As with the masteries - standard setup.
The Quintessence are the basic AD-champion runes. You can chose any of those three runes, but I prefere Physical Damage or Armor Pen. when laning TOP, Movement Speed when you are jungling.
Don't have much to say other than that.

The start of the game:

The allmighty starter item

Boots + 3x Health Potion

Against heavy AD like Zed, Garen or Riven you might want to buy Cloth Armor and pots.
If you're sure that you will dominate your lane, start with a longsword + 2 health potions or even a Doran's Blade in extreme cases, but I do not recommend this unless you really know what you're doing.

Core items:

You want your tier 2 boots as soon as possible, Mercury Treads or Ninja Tabis depending on the enemy team (Much AD and small amount of CC go for Ninjas, otherwise you go for the Mercury Treads).

The bread and butter of Jax and his, dare I say it, amazing burst and damage
Sheen
Phage
These two items makes Jax a beast, I can't even put words on how strong they are on Jax and his skillset. But of course these items won't make you win your lane if you got a Garen with 6/0/2 score at 15 minutes. The point is that the tankyness and slow of the Phage combined with the burst of the Sheen will make Jax superstrong - and his Ult. passive.
[ability=w champion=Jax]

Now I will go to the part where you got your boots and essential items
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I am superfed/dominating my lane:

Trinity Force
Maw of Malmortius
Ravenous Hydra


Trinity Force makes Jax's Phage and Sheen into a single item (HURRAY)!
+ You get the extra damage, AP, Attack speed, Crit. and that lovely 150% Sheen-buff.
It's an expensive item and makes you a glasscannon unless you buy more tanky items. It offers a lot of different stats that all benefit Jax, if you are fed this is the item to rush.

Maw of Malmortius is the best counter against AP champions or champions with a lot of magic damage. You want to buy MoM of you are laning against a Vladimir, Kennen, Shen or even a Garen (his ultimate does unbelievably high magic damage). It litterally saves your life, over and over again.

Ravenous Hydra is a "high stake - high reward" item, if you are not superfed, for example 10/0/6, and are dominating your lane and are able to gank every lane whenever you want). It's a superitem for you if you are so fed that you can tank the enemy team while slaughtering them with your Trinity Force + Ravenous Hydra combo. I do not recommend this item unless you and your team is stomping the enemy team... So be carefull with it, I'd recommend you to not buy it until you know it's full potential.
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I am nor fed or feeding, I want to be tanky:

Trinity Force
NOTE: If you buy Frozen Mallet + Iceborn Gauntlet you should buy something else than Trinity Force!(!)
Frozen Mallet
Iceborn Gauntlet
NOTE THAT THE TRINITY FORCE IS ONLY VIABLE IF YOU DO NOT BUY THE ICEBORN GAUNTLET!!
I usually chose Trinity Force OR Frozen + Gauntlet, never Tri + Frozen (but it works).

Frozen Mallet gives you health, damage and that SLOW. A pretty straight forward item for Jax. Can't add anything else than this.

Iceborn Gauntlet gives you even more slow, an on-hit effect and some pretty hardcore tanky stats, and the CD is a big plus!
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Situational items

Blade of the Ruined King
Black Cleaver
Wit's End
Guardian Angel

Blade of the Ruined King is the best item possible against tanky toplaners as Garen, Cho'Gath and Riven (usually). It combines really well with the Frozen Mallet+Iceborn Gauntlet combo.

Black Cleaver is a good item, maybe not the best on Jax but it does work well, you want to concider this item if you opponent is stacking armor and you don't want Last Whisper, TBC gives you some health, armor pen. and damage which all goes great on AD-characters.

Guardian Angel is an item that goes well on pretty much any champion and every build. It gives you tankyness, which allows you to bash your enemies even longer, and you got that ressurection passive that makes you a target not to focus. So it's both a direct defence item and a psychological defence.

Wit's End is rarly used anymore but it is still as good as before (that's my opinion). Lets say you are against an AP champion on top (or even mid [*hinting on a future build maybe]) and you already got Mercury Treads and Maw of Malmortius, what should you build now to counter that AP caster even more? Wit's End. But it might not be the most viable option for Jax, I think Guardian Angel is still a better option.

Controversial items

(you want to concider multiple factors before buying): Doran's Blade (stacking them, maximum 2)
Ravenous Hydra
Black Cleaver
Wit's End

Basic route:

Wolves - Blue - Wraiths - Wolves - Red - Gank

After that it's up to you.
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Items:

Basic jungler start with Hunter's Machete.

You want to rush

Items:
Madred's Razors
Boots
Phage
Sheen
Upgraded boots ( Mercury's Treads or Ninja Tabi)

If everything goes well and you succeed to gank a lot you an go for one ore two Doran's Blades, but it's optional. Doran's only scales well in early game, already in mid-late they are pretty useless so make the best of them if you decide to buy them.

If you are feeling gank-happy then buy Boots of Mobility, mobility-boots gives you the roaming-speed that you need to gank every lane very fast and makes counter-jungling even easier.
[DISCLAIMER] Don't buy Boots of Mobility Unless you really know what you are doing!

Controversial items

(you want to concider multiple factors before buying): Doran's Blade
Mobility Boots

Core of jungling items:

You chose between Trinity Force and Frozen Mallet + Iceborn Gauntlet.
After you have decided you can follow the regualr TOP-laner Jax-build.