Hi guys. I love League of Legends and one of my first Champ was Jax. So I decided to make a guide for AD- and AP-Jax. Personally I like AD more, because I like the scaling with Trinity Force and Atma's Impaler. But both builds are very strong and it depends on personal preferences.

I personally use this runes for AD and AP Jax:

With this runes I have the best early game possible.

You can also use following runes:
(only AP), (only in combination with Greater Mark of Insight) Greater Quintessence of Desolation (only AD)

It's important to get Nimbleness, because of your E.
AD: 21/9/0 (recommended), 0/9/21 (I personally don't like that build)
AP: 9/21/0

Note: Because of the 15% Mpen AP-Jax is scaling better with the Mastery.

Starting Items:
, , , (you can build it to Hextech Gunblade and Wriggles Lantern), (if you have manaproblems)

AD:
Core:
Strongest items: (if you rush it)
Armorpenetration: Enemy>100 Armor, Enemy<100 Armor

Wriggle's is good for 3n3, where you can farm the jungle easily and sometimes rush Dragon. In 5n5 I would only build it, when I face an AD oponent or the enemy tries to drown me in minions. When you build Wriggle's, I would do it as first item (after Doran's).

When you have problems against APs or ADs, you can build more Def-Items than Hexdrinker and Atma's Impaler or switch Hexdrinker to an Armoritem. Guinsoo's is a very good item against noobs, that let you build up your stacks, but against good enemys I don't bother buying it.

AP:
Core:
Strongest Items: (if the enemy stacks life)
Best Magicpenetrationitems: (if they stack Resistence, otherwise buy Abyssal Scepter)
Best Def-Items: ,

The problem with AP-Jax is the bad scaling with Def-Items. Abyssal Scepter has problems with Void Stuff, Atma's Impaler with Lich Bane and Zhonya's is extremly situational and Banshee's doesnt scale with your passive.

Recommended: ,
Situational: (in 3n3, when you're mates doesn't gank and to manage your bad early and to trick noobs), (Backdooring, in 5n5 to heal yourself in base)