Welcome to my Jax guide! In this guide, I will be focusing on the DPS damage output on Jax and his unique attack speed and hybridiness.
In order to get the full potential of this build, you might want to continue reading on. There are alternative paths for Jax depending on how you want to play him.

I chose the runes I did to take advantage of Jax's E. If you don't have enough dodge chance with Jax, his E will pretty much be a "ultimate" itself. You would rarely get the E in a fight with a caster type, so its pretty much a luck shot of them using a random basic auto attack or something.

Jax's dodging ability makes him unique. If you give him dodge masteries, and a few AP masteries, you'll dominate the battle field!

Path of a Hybrid-AD rounded DPS: Ninja Tabi, Guinsoo's Rageblade, Hextech Gunblade, Trinity Force, Lich Bane, Madred's Bloodrazor.

Path of a Hybrid-Healthy AD DPS: Ninja Tabi, Rylai's Crystal Scepter, Hextech Gunblade, Trinity Force, Lich Bane, Atma's Impaler.

Path of a Hardcore AP: Ninja Tabi, Lich Bane, Rylai's, Void Staff, Rebadon's Deathcap, Zhonya's Hourglass.

Path of a Hardcore AD: Ninja Tabi, Phantom Dancer, Trinity Force, Black Cleaver, Infinity Edge, Madred's Bloodrazor.

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I honestly don't care if you disapprove of one of these paths. Just don't use it. Use the main one. I use the main one most of the time. Don't whine to me saying "I did bad in this game ur build sux lololololl."

If you say that, you're probably some 12 year old kid sitting behind a computer laughing your *** off at every single comeback you throw out there thats just the same story of your life; You're a tool. If you DON'T say that, and you're 12 or younger, keep it up. If you don't be mean to people in life, a lot of things will go your way.

Jax's ability to deal high damage output comes from his Q and W. E is for a bit of damage, but also saving your *** or stopping ******s from running.

Ultimate - I personally don't think activating the ultimate does all that much, I only activate it when I'm trying to run. Maybe, in the future, when I get more comfortable with Jax, I'll find its use. But don't take my word for it that the ultimate activation is ****. It might not be. I just don't activate it.

Flash - Perfect to catch up to use your Q, or to run away. BE AWARE YOU CAN Q TO ALLIES.

Cleanse - If you stun Jax, hes useless. This fixes that.

Clarity - I don't see a need to. I haven't run out of mana yet.

Rally - ... Why did you even read this spell? Just skip over it. Its useless.

Clairivoyance - This is good, but let a support take it.

Fortify - Again, let a support or tank take this.

Exhaust - Meeeehhh, I don't really need it... take it if you want...

Ghost - Go ahead. You can never go wrong with ghost.

Heal - Well, this is good EARLY game and for first blood, but thats all. After that, its not all that useful.

Teleport - You shouldn't have the need to use this.

Ignite - Its okay, but Jax deals too much damage output to worry about people getting away...

Smite - You SHOULD NOT be jungling with Jax.

Revive - Oh heyul no.

Pros

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Good late game
His stun lasts pretty long
Massive damage output
Dodges save your ***
Easy to catch up with (Q) and run away with (Q)

Cons

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Not that great early game
Stunning renders him useless
Casters take Jax's uniqueness on his dodge away (Dodge doesn't dodge abilities)
Not a good dance :<