Jax is a hyper carry style top laner who exceeds at being an anti-everything. Jax benefits from both AD and AP, however going entirely one leaves you easily countered so a mix of both is best. The build in this guide gives jax the ability to vaporize people while being hard to counter. This build is not meant for every matchup but will work on most.

Kill the enemy carry, then anything else.

Jax's Q is a jump that can use to escape or initiate. It also benefits from his W.
jax's W is straight spammable damage that goes on the next basic attack or Q after use. Use with your triforce or gauntlet.
Jax's E can be used mid ability or basic attack and is useful for chasing\escaping it has a stun at the end and blocks all basic attacks.
Jax's R gives him armor and MR based on AD and AP so building damage makes him tankier. Also it passively gives him bonus AP on every third consecutive basic attack.