This Jax is Hybrid DPS with an insane amount of damage. Early game he is good at soloing because of his early damage. Mid-Game he can support and pick of enemies from ganks. Late-game if anyone dares to solo against him without a gank the opponent will surely die. Even 3v1 Jax still has a chance against them. Jax has weaker HP late game then most people, mages with nukes such as Ryze are usually his downfall...but only in ganks, as I said, Jax is invincible in 1v1 matches.

Ninja Tabi is a MUST for Jax, it not only gives him the Speed boost but increases his Dodge Chance, as well as giving the mandatory speedboost and a little armor. Guinsoo's Rageblade is an amazing item as well because it increases attack speed over time like relentless assault. I recommend getting Vampiric scepter before getting one of the two Guinsoo builds. Guinsoo's rageblade's build items are midly expensive and early game is hard to get. if u recall with about 450 GP go head and get vampiric scepter. After guinsoo's, its important to rush Hextech Gunblade. This will help you survive in battles, give AP and AD and give a free and better Exhaust. Lich Bane is more of a might as well weapon. Sheen is a pretty good weapon because of your combo empower and jump. But lich bane just gives some extra Mana and AP including the Sheen's affect. If your actually able to make it this far, Ryalais will help u survive even more! Plus it gives you a crazy good slow. Finish off with Rabadon mainly because it gives a ****load of AP.

Pros: He has extreme damage to most squishier characters early game and late game.
His DPS easily reaches 2.0 by mid game, giving him a bunch of lifesteal.
His Jumpstrike can help him escape and as well as Jump into fights.
With his counter-strike on, his damage his deadly along with an extra stun can easily take
down an enemy.
Cons: For enemies like Zilean, they have very far range and do massivev amounts of damage early
game, this is a major problem for Jax because his items are fairly expensive not allowing him to be fed is making jax pretty much useless.
Thornmail is another great downfall for Jax, unlike other DPSs, he can't run from a battle
Jax must stay and fight to regen his HP or he will easily die, and if an opponent has
Thornmail, then jax cant regen fast enough and he'll die unless your're lucky.

Train Jumpstrike first, then empower and then counterstrike. after that, look at the cooldowns (CD) of empower. Try to match its CD with Jumpstrike. Then after they are both equal, train counterstrike again. After training counter-strike, switch off between Jumpstrike and Empower. Train relentless assault whenever you can so your attack speed can rise.