Jax, no doubt the best duelist in the game as if right now. Has been seen as a hybrid champion. But then I found out how many people were playing Jax with HExtech Gunblade, and Gunsoon's Rageblade.
But i THink that pure ad Jax is wayy better because yu get maximum proc of your passive and your ult's passive.

These are the Basic Ad runes I use for laning and for jungling. For alot of sustain and also some damage output.

These are also basic ad masteries with some mr for laning against ap top champs such as Nidalee, the common Elise, Akali, and Singed.

THese are items that makes ad Jax ad Jax, since Jax's active ult give armor and mr, i don't put alot of things on armor and mr as much as on hp. These items makes Jax unkillable if your team is not snowballing very well, its fine to replace hydras with raduin's or gauntlets.

These skills allow me to be exceptionally well in lane against anybody. Alot of people max e right away, but the e isn't all that great until team fights.

Ghost is for chasing and procing aas on them, f you don't want to do that. Feel free to take Flash or Teleport.

Pros:
-Bully in Lane
-Good damage output through out the game
-Alot of sustain
-Counters everybody
-Hard to gank
-Low Cooldowns
-REALLY POWERFUL LVL 6 or LVL 3
-BEST at dueling.
-People underestimate your damage output (WUT A NUB)

Cons:
-Gets owned by aoes.
-Requires some skills
-Hard to farm and procing your passive at same time.
-Needs good map awareness
-Takes alot of risks when engaging.

Try to last hit like normal when playing passive. Try not to worry about you procing your passive and just last hit.

Before engaging in lane, get either 6 procs of your passive OR/AND 2 procs of your passive hits.
Press E, Q on them, Aa, W, E for stun, aa, aa, W.
Spam your W as much as possible.
Don't underestimate your damage output.

Easy Matchups
Fiora=easiest kill ever will ever have.
Irelia
Xin zhao
Rengar
Vi

Hard Matchups
Malphite
Singed
Garen
Jayce
Renekton