Welcome to my build. This maybe, not been used by many but I used it. I loved the way I kill all enemies in enemy tower. Ok, let's start.

As for runes, you can either go with ArP marks, magic pen marks, or attack speed marks, just based on personal preference. For Seals, dodge synergizes really well with your E, so those are a necessity. For glyphs I chose flat AP, for an early game damage and health boost, the bonuses of which outweigh an extra 5.85% CDR. For quintessences I have recently begun using dodge quints, which has been way better than flat health. I start the game with 12% dodge just from runes and masteries, and by the end of the game you're up to roughly 40% dodge, which is sweet.

Maybe some of you uses defensive masteries, but for me, I only use defensive masteries for nimbleness. I use offensive for greater damage output cause it gives added attack speed which is good for Relentless Assault, and armor/magic pene etc.

Jax isn't so strong early game. Buy Doran's Shield for higher health etc. Boots of Jax as always was Ninja Tabi. Use it for better using of Counter Strike. Then u should buy Hextech Gunblade for better life steal and spell vamp. etc. Use it with The Bloodthirster u will not die if you know how to use Jax properly, you can even kill enemies at their towers, just continue attacking enemis if you started because you have the right amount of lifesteal to resist tower attacks. Then buy Rylai's Crystal Scepter. It will slow ur enemy when u use ur skill and it gives added AP and health. Also buy Warmog's Armor to give added health and health regen. It will also give you added AD when u buy Atma's Impaler. Use this build to have the Ultimate Imba Jaximus Maximus. ^_^

It's easy to explain. It's a mid guide, most of them in mid are ranged. Empower will frighten them and Empower gives very high damage with only very few mana(20 mana I think). Counter Strike will stun ur enemy/ies. U can use it when they escape etc. Leap Strike, I only use one point for this skill early and mid game cause I only use it for escaping/engaging/chasing enemies.Then as always, your best skill is ur ss, Relentless Assault. It gives high ats, and damage output etc.
So this should be ur prior skill:
1.Relentless Assault-of course cause this is ur ulti, as every ulti was a priority
2.Empower-gives very high damage output early game - late game
3.Counter Strike-gives dodge chance and stuns the enemy, if you dodged an attack
4.Leap Strike-for chasing/engaging/escaping

I use flash, for escaping/chasing. And also Ignite for killing escaping enemies. Duh

Now with this guide, you can initiate with Jax, which is not an initiator and you can defeat 5 enemies with no teammates with this. U can also defeat Baron Nashor with yourself, ONLY!
Just don't greed, u can if you have all the items. Hope this helps!!! :D