Hi everybody, this one is my first build. Jax is the first champion I've bought, and he's my favourite one. I've used him for over 300 matches, so I think I am ready for publishing my build. This build is really similar indeed to Vasarius' one, whom I want to thank for inspiration. His guide has introducted me to the concept of hybrid build, which is, in my opinion, the best successfully choice for Jax. This guide will simply explain my choices, it isn't intended to teach how playing with Jax.

The runes I've chosen for AD and AP bonuses are both per level runes, instead of flat ones, because I think that, as Jax is a carry champion, he needs more bonuses in late game.

I've chosen Greater Mark of Scaling Attack Damage methodically applying hybrid concept. It grants a +22.68 AD bonus at level 18.
I've chosen Greater Seal of Evasion because you all know Jax is a dodge machine, as he has many combos with his dodge chance. It grants a 6.75% dodge bonus.
I've chosen Greater Glyph of Scaling Ability Power methodically applying hybrid concept. It grants a +27.54 AP bonus at level 18.
I've chosen Greater Quintessence of Evasion because you all know Jax is a dodge machine, as he has many combos with his dodge chance. It grants a 4.5% dodge bonus.

In the offensive mastery tree, I've completely ignored Deadliness and Lethality: Jax really doesn't need bonuses for his critical strike. I've ignored Offensive Mastery too, and of course Plentiful Bounty and Improved Rally. The other ones are maxed out.
As long as Exhaust and Ignite are my chosen Summoner Spells, their related masteries (Cripple and Burning Embers) are a must to have. Burning Embers also combos with Jax's AP bonus - in early game this simply rocks.

The defensive mastery tree is quite standard for Jax: nothing new to say here, I've obviously maxed out Evasion and Nimbleness, always for the fact that Jax is a dodge machine.
I've not forget to max out Resistance too. The one single point on Hardiness was required, but isn't very useful.

This part is incomplete.

Ninja Tabi are a must for Jax, incresing his dodge chance by 12% (actually the only item granting dodge chance bonus).
Guinsoo's Rageblade is the first hybrid item to buy for Jax (+195 HP), nothing to say more about how this one rocks.
Hextech Gunblade is the second hybrid item to buy for Jax (+330 HP), nothing to say more about how this one rocks.
Trinity Force is the icing on the cake for Jax. Its power is enormous, it grants anything "Jax really needs from an item" [cit.].

Optional items are quite standard too: Mercury's Treads, Hexdrinker and Banshee's Veil for granting huge magic resist bonuses against heavily magic-oriented parties.

This part was one of the most difficult I've encountered while creating this build. Jax can't even harass properly without the basic Leap Strike + Empower combo. That's why I always put the first two level points on them. Third level point goes to Counter Strike, granting huge and useful early dodge bonus for harassing. I've chosen to spend level 4 and 5 points on Leap Strike in order to synchronize its CD it with Empower CD, and I've tried to keep this synchronization with level points from 12 to 15 and 17-18. Level points from 7 to 10 go to Counter Strike, in order to early maximize Relentless Assault's effect - which obviously takes level 6, 11 and 16 level points.

The Summoner Spells I've chosen are Exhaust and Ignite. The choice was between those two or Ghost and Flash, but after many hours of gameplaying I've decided to pick the two above, even considering my choices for Offensive Mastery Tree (and the previous cited combo). I know they're both offensive Summoner Spells and that I haven't got any escape skill, but I think Jax can manage - more or less - escaping with Leap Strike.

I know this is not a revolutionary guide, but I hope it can help someone in developing a better one :P
All credits go to Vasarius, source of inspiration for this guide, and to my game mates Silverounet, Dexterminator and Azurrr: without their patience for playing with me so many games, this guide could have never seen light.