Well, this is my first build, so it's kinda hard for me to describe EVERYTHING....

Well, to introduce my self, I'm a Jax and Yi main person who loves to play tankers and assassins. Jax caught my eye around 3 months ago, and I have bought it when it was still 6300 IP (really, Riot immediatley changed the price =.=). So for quite a few days, I have played jax a lot of times and these two builds that I have used always worked.

My choice of runes...

Well, you can notice that both AP and Hybrid Jax have the same runes. Well the thing is, most of jax's attacks are based on AP and Dodge. By increasing the Dodge chance, you will be able to use his Counter Strike so that you will immediatley kill the enemy unit. Magic Penetration is something that I might change later on. Based on my experience, the Magic Penetration doesnt do much as having more AP, but it depends on how you like it.

My masteries are 9/21/0, receiving dodge chance and Nimble to increase his movement speed during combat. Getting Exhaust is very useful since as soon as he jumps on his enemy champions, he can't receive dodge unless getting hit by minions or by enemy AoE damage. getting decreased Cooldown is also important since his Leap Strike at lvl 1 would have 10~12 second cooldown. Runes for cooldown reduction is an option to replace Magic Penetration. Focus most of his masteries towards Ability power.

First item to get at all times is a Doran's Ring. The recommended build says Doran's Shield is much better but trust me, at 600 hp with like low AP is really bad. With Doran's ring, you get +100 hp and additional hp because of his passive.

Ninja Tabi is the second one I received since his low def needs to be fixed immediatley.

The third item is a necessity. A Guinsoo's Rageblade is a VERY, let me requote, MUST HAVE item for jax. His ulti's passive is that every three hits, he deals extra damage + his ability power. By owning Guinsoo's rageblade, you are able to stack more att speed and AD. With 10 Stack of his ulti and 8 stack of Rageblade, you get your att speed up to 2.104 or maybe more.

A Rylai's Crystal Scepter is also useful in killing champions. With the Passive Slow ability, he can jump on a champion and start stacking Rageblade and Ultimate faster. It also increases his AP and HP with again additional HP from his passive.

Hextech Gunblade is my 4th Item for the AP build. It's slow active is again usefule since it's good to kill a person faster. Its increased AP and AD with lifesteal makes it almost impossible to kill Jax. People might rush to a Hextech, but I do not recommend doing so, since it will make you harder to farm. Getting Rageblade will make it so that you farm faster and enable you to buy more items to KILL.

The Hybrid build will receive a Frozen Mallet. It's AD really doesn't do much to his abilities, so having AD with Health would be more useful, so I have chosen Frozen Mallet. It's HP and AD will make it so that your HP is around 3800~4000.

Now for the Final and last item. The AP gets a Rabadon's Deathcap. People might say that I'm crazy (please don't comment that...) but trust me, with his abilities being mostly dependent on AP, having a Rabadon's is not that bad. It increases hp and AP will make you almost INVINCIBLE.

The Hybrid gets Atma's Impaler. The unique passive will do a Double Stack. The passive will increase AD based on his HP and his passive will increase his HP based on his AD. When thinking about it clearly, people might say "well doesn't that make it Infinite Stack?" Well, Riot is not a dumbass group so no, it stop after double passive.

Situational items are to be considered. Some people recognize Jax as a tanker so it's a good thing to sometimes buy a Thornmail or Rod of Ages. it depends based on your enemies though.

I tend to master Leap Strike first since it's the only skill that adds your AP and AD. With both AP and AD being a necessity to Jax, he will do about 150 damage at the beginning. 2nd skill to master is Empower. With Empower and Leap Strike combo, you will deal massive damage. Empower can be used with Leap Strike but it's only one hit duration so try not to waste it. Before mastering any of the skills, get Counter Strike so that you will receive extra dodge chance and atleast be able to stun the enemy.

Now, this is the part where I might get a little fussy.

Summoner Spells can be changed from one to another. Flash is a very useful spell so that you will flash and jump further out to kill the enemy. Jax is also a slow type. I mean just look at his size... Flash is a must have for jax.

Now, Exhaust is good to use, especially in team fights so that you can attack the weak one first.

Well, when getting in a team fight, always hit from the back. Jax is a surprise attacker that can go from bush to a jump kill in an instant. Jax's mission is to be a ninja where they can't expect where he'll go. Always go for a gank. Doing a head on fight is a very bad use of Jax. I have experienced many times first hand and I swear I have died so many times...

A 1 v 1 is also a good use of jax since he can easily stun and kill one to another.

Now, your teams. Your team must be a pre-stunner, one's that don't require any circumstances to use it's skill. Jax's stun is not much reliable in a jungle team fight. Not a lot of minions or creeps to give you stun. First you need to have pre-stun and attack, after just stun him when he gets to his lane by dodging minions attacks. Remeber, minions will attack you when you dare to hit the champion.

Well, that sums up my first build.

Please comment how I could improve my build and please compliments~ xD