Since Jax is a hybrid champion, that means that he builds both Ability Power AND Attack Damage items. For his masteries to pump out the damage I spec 30/0/0. Now some may think: "Having all 30 points in one tree is stupid". When you are ROFLstomping the enemy team you wont think having all 30 points is stupid. I build all the way down row 3 and row 4 of the Offense tree because it gives constant damage whereas skills like Demolitionist or Lethality aren't very useful for jungle Jax.

If your team is lacking a lot of tanking capability, I suggest going the traditional 21/9/0 build, putting points into the Offense tree to reach Executioner and putting the resting into the first few basic health, MR, and armor stats in the Defense tree.

If your team is tanking impared then either pick a different champ or if you REALLY want to play Jax go 9/21/0, putting points into damage reduction, health, MR, and armor stats until Juggernaut . Put the rest into AD stats in the Offense tress.

For jungling, start out with cloth armor and 5 health potions. This gives you armor as well as a lot of HP pots to be effectively keeping up with the jungle. Afterwards, either get Boots for quicker ganks or Madred's Razors for an easier time clearing the jungle. Finish your boots with either Mercury's Treads or Ninja Tabi depending on how the enemy teams line-up is. If it is equal, I suggest Mercury's Treads for the additional Tenacity but if they have 4+ AD champs then get Ninja Tabi for reduced damage. Finish your Early game with Wriggle's Lantern and grab a Sheen.

Start building Guinsoo's Rageblade for both AD and AP as well as the passive that compliments Jax's own passive. Once finished, Get a Phage and finish Trinity Force. From there you can start really dealing out the damage with high bursts.

If you played your cards right early game, Jax will explode almost anyone that isn't a tank in late game. Say goodbye to the enemy squishies if they aren't being escorted at all times. Start building Hextech Gunblade for the extra damage and another nuke :3 Afterwards, finish your build with either Guardian Angel, Infinity Edge, or Rabadon's Deathcap. Depending on what is going on in your game, each item is viable. If they build a lot of magic resist/health then get Infinity Edge for more AD and crits. If they build a lot of armor/health go for Rabadon's Deathcap so you can put a huge dent in them with Empower and Grandmaster-At-Arms. If the enemy team is bringing you down quickly, grab a Guardian Angel for extra armor, MR, and the ability to be revived if u get gunned down quick.***KEEP Wriggle's Lantern*** Even though it may not be as good as other items late game, The ward function has saved me so many times. Once you get good with Jax and using his item abilities, use lantern to escape tight situations by throwing it over walls and jumping to it.

Rylai's Crystal Scepter is viable for it's health buff and AP for your Grandmaster-At-Arms and Empower. It also slows enemies hit with your abilities, allowing you to sustain the damage and close gaps effectively.

Maw of Malmortiusis viable for it's AD, MR, and both of it's passives for defensive capabilities. Grab this item if you are having a hard time 1v1ing with AP/AD carries.

For jungling, start with Counter Strike. Immediately after the leash wears off, pop it and you will dodge, stun, and loose almost no health. For level 2 ganks, I recommend that you get Leap Strike so that you can jump and stun for an easy first blood kill. Then go back and forth leveling Leap Strike and Empower. Start at Blue -> Wolves -> Wraiths -> Red -> Golems

Leap Strike is a great skill overall. It is utility and offensive because you can jump-to/damage enemies AND you can jump to allies/wards. Great mechanism for escaping and catching up.

Empower is Jax's nuke. I personally love this ability because it can stack with Leap Strike and you can use it during Counter Strike. It has a very low cool down and does massive AP damage.

Counter Strike is one of the most unique abilities in the game because it is the only dodge ability. Once activated, Jax will dodge all normal attacks and can still attack and use abilities. Once the duration of the skill expires, all enemies around Jax are stunned. This ability is amazing for ganks because if you time it right you can jump to an enemy and immediately stun them. Active Empower then Counter Strike and lead into Leap Strike. When used correctly this skill becomes one deadly QQ creator.

Jax's ultimate ability, Grandmaster-At-Arms, helps him dish out the damage quickly. It's passive ability gives him a huge AP nuke damage on every third hit. On activation, he gains a large armor and MR buff. Active the ability when going into team fights to reduce damage and stay in the fight or when in close 1v1s this will give you the edge.

Flash is a very common, yet very useful, summoner spell. It allows for an easy escape and a deadly gap closer. I recommend this highly on Jax.

Smite is the typical jungler summoner spell. It helps clear the jungle mobs quickly and effectively while giving you bonus gold if the mob is killed with it. I recommend this highly if jungling.

Ghost is useful for its speed buff that you can use for effectively ganking,catching up, or even just getting from one place to the next quicker.

Igniteis great for it's healing debuff and the extra true damage.

Exhaust is great for the slow and the extreme AD/AP debuff for the duration. Works best during 1v1s.