I made this build to teach you guys how I play Jax,most people find this build odd because at no point do i get a Guinsoos Rageblade, personally id prefer to always have the flat ap and ad and as instead of needing my stacks,getting stunned or supressed in a teamfight ruins your guinsoos stacks and your ulti stacks making you basically a lot weaker.

Personally i like to get the cloth armor and health potions first because it can easily build into my boots quickly. Side note if there is 4 characters that are ap on the enemy team, especially if your sure your not laning with the ad: get your boots, its just easier for traveling back and escaping ganks if your flash is on cd.I like to rush the revolver for the simple fact of it giving spell vamp, this comes in incredibly useful.I get my madreds to add a harsh amount of damage to meat shields and tanks.The malady conveniently gives 2 things Jax craves as and ap.I like the sword of the divine because of its passive effect basically adding an extra amount of bang onto your ultimate.The quicksilver sash is just an amazing always useful item, whether warwick is using his ultimate on you you've been stunned poisoned slowed ,whatever the quicksilver sash with 1 press of a button removes all debuffs.( I suggest moving it to the 2 or 3 key because they are closest to the q-w-e-r for your abilities to quickly react.)

Personally i like ignite and exhaust because they are very useful early game to get your first blood and are useful against characters like warwick and swain to cut off the healing with ignite, also exhaust is helping to slow down fast attacking characters like Master Yi before he has popped his ultimate.
Teleport is also a very useful skill for transport and maintaining feeding off minions
Flash is good for starting or escaping ganks
Heal is also helpful to get the upper hand over a person in a fight

Pros: Overpowered
Wrecks any tank if you have madreds
Gets tougher as the fight progresses

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Cons: Getting stunned or suppressed late in a fight can really hurt your fighting.
Dependent on getting items.