Not Updated For Current Season
The masteries shown here are not yet updated for the current season, the guide author needs to set up the new masteries. As such, they will be different than the masteries you see in-game.
This Jax build was made up on the fly during a ranked match and ended up being much more than I had thought it would be.
I will admit I am not the most knowledgeable about runes but this seems to be the most ideal setup. You can adjust anything you think would be better but I highly recommend you keep the dodge runes.
For masteries I go with 21/9/0 for early damage and magic penetration, as well as dodge and a little bit of magic resist.
With this item order you start the game off with more ap. (If you watch most tanks early game all they care about is health and armor.) So your empower+jump even damages tanks quite a bit. As the game goes on the tanks try to adjust their build by buying magic resist and this is where the madreds+bloodthirster come in. You throw them off by adding powerful dps items and destroy anyone who challenges you. If you are successful in completing this build I would suggest trying a little 3 vs 1 =P. (Learning how to play Jax in custom is essential to doing well in normal/ranked games.) Also, you shouldn't be frightened by the health up top because Jax's passive increases his health by 3 for every point of attack damage received from items and by 2 for every point of ability power from items.
I chose exhaust/ignite because I like to get first blood before the minions spawn but feel free to change them to what you feel comfortable with. Flash and Ghost are very helpful with catching up to fleeing enemies or running away from ganks. Survivability is key in completing your build.