BEFORE JUDGING THIS GUIDE, READ THE ITEM EXPLINATION. My name is Zandrey, and I'm from Sweden, note my core language isn't english so i apolygize in upperhand for spelling and grammar misstakes. I've liked Jax for a quite a while but it was in Season 3 and when I bought the Jaximus skin my gameplay reallt started shine.

As your staring item you want to buy 6 healthpotions, 3 manapotions and 2 wards, because many toplaners will try to bully you pre 6.Rushing the trinity force as your first item gives you alot of utility, diffrent stats and ofcourse tons of damage. Here is the diffrence between my guide and other guides! I NEVER buy tier two boots. Because a trinity force and Zephyr gives you a base movement speed of 408 even without tier 1 boots. More then most of the caraters in this game. Plus Zephyr gives you tenacity. And the ad you got from items gives you armor when you ult. The great thing about this is that you get a extra item, plus you got more movement speed then the one's you're chasing. I usally buy gunblade because the ap it gives you transfers to extra magic resist when you use your ultimate. I love Warmogs because it gives you 1000 hp and a awesome regen passive. Great item always get this. Guardian Angel got nerfed abit. But now you respawn with a diffrent amount of hp depending on your max HP which you will have a lot of. In most cases I would buy Maw of Malmortius because of that awesome shield, damage, and magic resist. Buffing your ult alot, but also you'll get really strong when you respawn with your Guardian Angel. Plus don't forget Bluepot, Redpot and Orcale.

Attackdamage marks because they are the one's who fit Jax the best.
Scaling Magic Resist blue because most of your opponets will be attack damage based so taking scaling blues helps four your late game.
Armor Seals because most of your opponets deals attack damage, but also minions.
Movement Quints because they help engageing, disengaging and they are overall strong trough out the whole game.

In my opinion this is the best runepage for Jax,they give him som takyness but alot of damage. Just rember to chnage between magic resist and armor in the defensive tree.

I prefer Ghost and Ignite for killpower and ghost for escpaing, chaseing and late game teamfights.

Flash works, but I don't like it as much.

Exhaust works if you're up against a really attackdamage heavy oppenent or team.

This depends ofcourse on your team and the enemyteam but what I found have worked best in most cases is to try winning your lane, ask for a gank if needed. Then try to farm up and become as beefy as possibly, try splitpushing and take towers. Your attackspeed passive is great for that, and the sound from your ultimate is so satisfying. Remember to use your Empower as a atack reset. I dosn't do extra damage though. In teamfights you want to try focus down their carries, in most cases their ADC. Ghost really helps here.

Start of with your counterstrike (E), becuause it's almost everytime strongest at lvl 1. Then your Leap Strike (Q) to escape ganks or engage depending on the jungler and your lane opponent.
You want to max Empower (W) because having a auto attack reset every third second is so strong, and it works perfectly with your ultimate (Grandmaster's might). In almost every case you want to max your Counter Strike second because having a dodge and stun every ten seconds is really powerfull. Plus it deals more damage than Leap Strike.