Hello guys. this is my first guide and I would like to show a nice build for Jax.
AP Jax is funny how devastating!
I hope you can find some utility in this guide. Nice reading.

SPACESPACE

PROS: -Good harass potetial. -Nice amount of instant damage with the combination of Empower and Lich Bane. -Nice surprise factor. -Good mid-late game. -Really fun to play and see the enemies nearly shotted (if you're very fed).

CONS: -Need to be mastered. -Can be Countered and be quiet useless or hard to play. -Quiet squishy. -Early farming is very difficult.

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OFFENSE TREE Tier 1 // First of all you NEED cooldown reduction because you have to spam as fast as possible your Empower but also Leap Strike; therefore 4 points on Sorcery is a must. Tier 2 // Expose Weakness is pretty helpful to take an initial first blood with all your team if you use your Counter Strike at level 1. The choice of Mental Force is simple, more AP = more power. Tier 3 // Spell Weaving synergize well with your abilities that use basic attacks like Empower and Master-At-Arms. Arcane Mastery helps you in early game with more damage. 3 points on Executioner will help you to get kills easier. Tier 4 // Like other masteries Archmage make you to do more damage. Tier 5 // Penetration is the most useful thing in early game and Devastating Strikes give what you need. Arcane Blade is pretty useful in late game cause you can synergize it with all your abilities. Tier 6 // Of course 1 point in Havoc to do more damage that don't hurt.

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UTILITY TREE Tier 1 // Fleet of Foot helps you to chase and get kills that you need because in early game you can't farm but also it can help you to escape. Meditation isn't a must but, if you want to farm with your abilities, it can help you with a bit of sustain. Tier 2 // Flash and ignite more often? Summoner's Insight help you to take kills and escape so why not?... For lane farming you need sustain that Alchemist could give. Tier 3 // Culinary Master fed you with cookies :3 want more?

You have to start with Counter Strike because with it you can win an early fight with the multiple stun. You can also start with your Empower for a better farming but i don't recommend it.
Of course the most important ability to develop is Empower because it is the bread and butter of your fighting style.
Master-At-Arms is your cup of tea because it deals a lot of damage that escales only with ability power!

My favourite combo after purchasing Lich Bane is using Counter Strike then Leap Strike after Empower and in the end let your Master-At-Arms do his job.

Counter Strike >> Leap Strike >> Empower >> Master-At-Arms

If you do this combo correctly you will deal a lot of damage and active the Lich Bane 's passive on every strike!

- Flash is a must for escape and chase. It helps you with your combo if you need and if you are dying because you're squishy you can save yourself by using Flash through a wall.

- Ignite use it for take kills without excessive risks.

- Barrier is not my favourite spell but, if you are against champs with a very strong early game, it can save you from a easy die.