The Tanker Path:
Boots+pots, Bilgewater cutlass, Finish boots, Sheen, Aegis,Guinso,iceborn gaunlet, hextech then runic bulwark and guardian angel.

The Norm:
Boots+pots, Bilgewater cutlass, Finish boots, Sheen, Aegis,Guinso,Trinity Force, hextechgunblade then runic bulwark and guardian angel.

As the title describes this is simply a quick cheat sheet on how to build / itemize on Jax if the item build finds any popularity i will elaborate further and explain matchups and such. This build is intended for top lane strictly, Start with boots 3 then go directly into a bilgewater cutlass then a sheen, Finish boots then finish trinity then build guniso then finish gunblade and then build aegis after that build GA and Bulwark, if your doing atmogs then dont build GA your absolute core items are Boots,gunblade,guinso,trinity. Boot Enhancments are optional and will not effect you that much, my personal favorites are Alacrity because the constant buff accounts for a boot of swiftness its really useful. The last two items are optional from the items i have listed, as far as summoner spells go ignite as good as well as exhaust but ignite got its cooldown nerfed so i find exhaust more consistent even though the effect was nerfed as well but since it retains a realtivly short cooldown i find it the most useful. Good luck out there on the fields of justice and kick some ***!