I have played roughly 300 games with Jax and I have to say he is one of my favorite champions to play as. At first I built him with heavy hybrid items, the standard rushing Rageblade and Gunblade followed by a Phantom Dancer and Defense Item. After getting a relatively decent grasp of him I started to experiment with things and found Jax's, in my opinion, burst potential is wasted if you focus on a simple hybrid build. Without further ado, I present my Night Angel Jax Build. Hope it helps.

Lets Start here. Considering if you read this first you will be able to determine if you want to give this a try or not, depending on your style of gameplay.

>Pros
-Great Early-Mid-Late Game Burst
-Half Health most squishies
-Almost never loses a 1v1 against a DPS because of very high dodge chance
-Can stun the entire enemy team
-Lamppost > Them

>Cons
-No answers to a very high magic res. team
-Glass Canon, though he does have escapes

I choose these because most of the damage this Jax puts out is Magic therefore Magic Pen. Marks, Dodge is always a must for him and the early Game ability power I like but you could also take flat Magic Resist.

Most Jax like to go with the Rageblade first. I find the Leap+Power+Sheen proc an insane amount amount of damage. After that the Rageblade is standard of course on Jax because if its great synergy with his ult. From there build a Lich. You will almost never lose an auto attack fight, unless of course your fight a fed Tyrn. Rabadons almost never gets finished past the Rod because they will surrender. You will simply be Leaping around nearly 1 hitting their squishies and just owning all of their faces.

Note: These items are just my mainstream build. I often adjust after the Rageblade if certain Champs or Archtypes are really messing me up. Ex. Thornmail, Banshees Veil

Ghost: Mostly a personal choice on this one, I love Ghost. Be it for escaping chasing or getting into a team fight more quickly. Can be easily replaced with Flash.

Exhaust: Shut Down carries. Stop them from running. Nuff' said.

Not going to go into the other spells because you all know what they do and they are mostly preference to what you like to do in game anyway.

DO NOT initiate a team fight. This happens to me quite often when I feel very string and cocky. You can be the judge of jumping into 2v1s because I often win those, however do not do anything too crazy unless you know where the rest of their team is. If you need to hold off for a second in team fights too hop in and last hit the carry. But dont play too careful you can stun the entire team which is insanely helpful for your team.