So. I have always loved Jax, and he was one of the first champions I bought. This was a long time ago, before the patch that changed him. Back then the idea was to get as much dodge and attack speed as you could, and hope that the other team was made of auto attackers so you could stun every two seconds. He is a different character now. The way I like to play him is as a hybrid, although mostly AP champion. All of his moves stack with Ability Power, so it only makes sense to build it on him. However, he is an auto-attacker as well, so some AD is definitely necessary, and I think that's why pure AP builds don't work very well.

I go all out offensive in masteries when it comes to jax. For i believe that the best defence is a good offence :3 A jax that scares your enemy due to your huge damage is better than a tanky jax don't you agree? So i use 29/0/1 masteries.

For runes go for armor, magic resist and armor penetration runes. For Marks i get armor penetration. For Seals go for armor runes. Lastly, for Glyphs go for magic resist. For the Quintessences it's really up to you. As for me I prefer to get 3 flat +4.95 Ability Power Quintessences. These runes will surely make you tanky in the early game. This will help you lane longer rather than waste time recalling to your base just to regen :3 You really can take a lot of punishment before you really need to go home!

These are the summoner spells I find myself most often using, although I almost always use Flash and Exhaust.

Flash: Perfect for escaping through walls, flashing to get off that extra leap, just an all around good summoner spell. I label this summoner spell as a MUST GET spell.

Exhaust: This makes it impossible for another melee character to 1v1 you, and makes it a lot easier to catch up to people when they start to run away.

Ghost: Sweet for chasing, running away, getting places faster. I usually switch between this and flash depending on my mood, hell sometimes I grab both.

Regrowth pendant- Gives your hero fast regeneration in the early game. Some people consider Doran's shield better but I don't. That is because I'm aiming to get a philosopher stone ASAP to help you with both health and mana regen.

Ninja Tabi-Nice cheap boots, they give some nice armor as well as needed dodge. Gives your hero a better chance of dodging enemy attacks, helping you land stuns on both creeps and enemy champion of they fight you. Making it a MUST BUY item for Jax.

Hextech Gunblade- Excellent item, albeit expensive. Great AD and AP for a sweet health boost, a great damage boost, and the lifesteal and spell vamp lets you actually live in full team fights, where Jax isn't really all that amazing, mostly because he gets focus-fired down pretty fast.

Guinsoo's RageBlade- Absolutely a key item for Jax. It synergizes very well with your ultimate, getting your attack speed up super fast, while providing more AP. The AD and AP gives over 200 health from your passive too.

Shurelya's Reverie- This item builds out of your Philosopher's Stone and boasts a multitude of stats. The health, CDR, and regenerative abilities all benefit Jax greatly, and the active will help your team initiate, chase and escape with ease. This active is also very helpful to Jax, as it allows him to easily get into melee range to use his abilities. It also helps you to get the enemy champion within the range of you leap strike skill. At the end game you can sell your shurelyas and buy either Warmogs or Banshee's Veil.

Rylai's Crystal Scepter- This item is so freakin sweet. It bulks you up like a champ, giving you 660 health including your passive, only 80 less than a frozen mallet would give. The slow is awesome, and it lets you get kills you usually wouldn't have and escape when you usually would've died.

Malady- is another key item for Jax. It gives a big attack speed boost and decent bonus magic damage. The primary reason why I get malady is because of it's passive. It shreds the magic resist of the enemy making you ultimate literally SHRED the enemy champions health.

This build preferable works for Jax when he solo lanes at top. Empower > Leap > Stun is the best effective combination Jax's skills. Chances are you'll get FF, or they'll start to attack you because they realize you're decimating their team because of you annoying stun. If you do find yourself getting focused (Odds are you will be), leap outa there or use your Shurelyas to flee for a moment. Then run back in if they stop chasing you. But still. *******. When you attack 2 times a second, in 5 seconds you can just devastate a squishy enemy champion within seconds.

Early game-Firstly, Jax isn't an early game killer so always stay defensive and earn as much money as you can without risking your own safety. I preferable tower hug then use leap and empower to last hit enemy minions. On the other hand if you enemy counterpart in the lane is squishy always try to land your basic combo force them to back off. NOTE: I only leap on enemy champion when my stun is ready. If the enemy champion is melee and can't tank you on ALWAYS remember to Zone them out by scaring them off by moving near them. This greatly improves you chances of getting your key items earlier than expected.

Mid-Game- Lane as long as you want, but as soon as team action starts, go right to your team. Try and run around ganking, and in team fights always focus the squishy. Leap, empower in, stun then run out, or keep beating on them if their team allows it. Focus on getting enough money for Guinsoo's and Hextech, and go for lizard and golem whenever they're up, especially the enemies. But always consider the benefit of the team when it comes to Golem or Lizard buffs. IF you have AP champs who need CD reduction and mana regen don't hesitate to give it to them. If they need help you can even lend them a hand in getting the buffs. You can take down Golem, Lizard, and Dragon really fast after you have Guinsoo's. In this mid-game phase Jax is great pusher due to his ultimate. Always try to destroy as many towers as you can SAFELY. Remember you're stun is a great help when it comes to clashes for it doesn't just stun 1 but all enemies around you. So always play safe! :) Oh yeah, I almost forgot! Always use you hextech gunblade to help slow down or even kill enemy heroes that +300 damage and slow is a great help!

Late Game- At this point you should have most of your items, at least Guinsoo's, Hextech Gunblade, and Shurelyas. Focus on wrecking havoc on squishy champions in fights (Leap-empower-Stun should take away anywhere from 1/4-1/2 or more of their health, especially to champions with minimal armor and magic resist. Put up wards at buffs if necessary, and wait to see if you can gank enemies there (Always ward dragon if you can't kill the dragon alone to avoid making the enemy team get the Dragon money bonus to team). But even though you have this guide it still depends on your teams cooperation and support to see who will win. By the end game your Jax should have max 2.5 attack speed with the bonus of you ultimate, Guinsoo Rageblade and Malady. :3

Never initiate unless you have the upper hand by having a ready stun or you have other team mates to help take-down the enemy champion . You will die if you initiate a team fight without a plan. You are an assassin, to fly out of bushes and the mists to 2 hit their casters, not someone to take the brunt of the damage. The only time you should every initiate is perhaps for a gank, or if it's 1v1 and you know where the other 4 team members are.

- Don't think you're invincible. I have this problem. All too often I do crazy things like running at fights my head knows I can't win, or chasing people way to far. Try to be cautious. Don't do stupid things. Yes you have a stun but you can't stun constantly, and if they slow you chances are their team will jump on you and you will die.

- Play Smart. Don't be stupid. Don't start fights you can't win. This advice should hold through with any other champion as well.