Not Updated For Current Season
Jax: LEGENDARY!!! (3v3)
This is only how I play Jax. it tends to destroy people unless you are against an almost completely non-physical team.
Try to get a solo lane by yourself. Jax is not that amazing in the early game so be cautious against powerful early game champions. However, with the health quintessences and vamp scepter you are not squishy so try to stay in the minions and harass the other player with leap. Once level 3 you can try to kill the opposing person if they are physical damage. if you start getting low stun them and leap back to the minions. If you are killing them ghost so they can't get away and stun when you are in range to stop them.
Masteries are absolutely key for Jax, the extra damage and dodge from a lvl 30 book can save your ***. 21/9/0 is normally the way i go, it is actually the only way i would build Jax.
Vampiric scepter: Great for staying in lane and getting early kills
in the early game try to keep 3 Health pots and 3 mana pots on you so that you can stay in lane.
Ninja Tabai: Lots of dodge.
Guinsoo's RageBlade: Now alot of people will say if your going physical damage why would you want an item that give's ap, the reason is your ultimate, for every ap you have your 3'rd strike hits that much harder, not to mention ginsoos will boost your attack speed in fights.
Zeal/Phantom Dance: Zeal/Phantom Dancer gives you some much need attack speed, crit %, dodge %, and as an added bonus, movement speed! (Rape Item!)
Infinity edge: I know you already have the scepter for a Bloodthirster but the crit, crit damage, and damage will help you nuke much faster with phantom dancers your crit will be over 50%.
Blood Thirster: The damage/lifesteal will make you pretty hard to kill and you are probably fed at this point. Usually games end before this(rage quits from being destroyed or surrender).
Madred's Blood Razor: This may seem odd but with your Attack speed is so high with your ultimate stacked+rageblade+Phantom Dancers+this you will be proccing your ultimate A LOT and with Bloodrazor especially against a tank its just more nuking.
You may need to adjust the build based on what team you are against.
)Other recommended items
Last whisper: those pesky armor tanks...
Sword of the divine: oh look another Jax...
Banshees Veil/Mercury Treads: AP champ team...
Leap Strike: Best to level this up as fast as you can as it starts out with a long CD that decreases quickly. Needed for survivability and chasing people down.(you can leap to wards)
Empower: It is powerful and good early game but maxing it out is not a large increase get it but leave it at rank one for as long as needed to level up other things.
Counter Strike: Key spell for jax: 10% dodge on first lvl passive, that is just beastly, not to mention after a dodge you can activate this for a short stun, this is extremely useful when being tower dived, tower diving, or in team battles.
Relentless Assault:The reason Jax is so powerful. extra damage every 3rd hit and attack speed, amazing.
That's my build. If you have any comments, questions, or just want to rage against it, please do, if you like it please give me a thumbs up.
In game name, asamu, if you have questions. (US server)