Heya! well i've been playing a lot with Jax latly and to be honest i've tried a little of this and that ranging, from ad jax, to explosive ap jax, to a couple of hybrids, to tank builds, they all have their ups and downs but primarily i decided to try a little something, and take full use of the ap ad lifestea and spell vamp of a couple of items (mostly one :P)

the result? and off tank jax that litterally brings a whole other meaning to "OP" or "not dying" why? well we all are aware of jax's passive that gives stunning amounts of health, then also and his amazing amounts of damage, so i thought to myself, "ad does lots of damage over time, ap does explosive damage and explodes the enemy, hybrid brings both together but you die quite easily, and i need to make somehting out of the damage, then i looked at the Hexteck Gunblade and noticed it's unique ... which made me look twice and notice that the lifesteal and spell vamp aren't included in the unique, and at that moment i realized, tons of damage + overwhelming amounts of lifesteal and spellvamp = lots of returned life and survivability. and thus i abused the system and incorporated 3 hextecks, yes 3, simply because i get 60% lifesteal and 75% spellvamp and tbh i managed to solo baron with just a nashor's a hextech and a semi built guinsoo's at level 14 (lolwut? O.o") don't get me wrong im not trying to brag, im just showing you the true power of the hexteck.

Note: the item build sequence shown above is the usual one, but take into consideration it varies dramatically from game to game, sometimes rushing hextech othertimes guinsoo's, but the major outline stays the same

Note: I cannot stress how much you have to analyze the situation and muy the items acoordingly, fail to do so and this will suck bad for you, but get it right and you can easily score pentakills in teamfights and near towers.

Note: The reason i use so many hextechs is simply because Jax uses every bit to his advantage, from the extra life to the extra damage to the lifesteal, because honestly with jax it's a matter of jumping in, them hitting you a little and you smash them back and watching your lifeback magically reappear.

Swiftly Moving on

Alrighty Rune Time for runes i do the following

9 Greater marks of Desolation:
Helps with the whole issue of killing minions and attacking early game

9 Greater Seals of Evasion:
Dodge seals, enough said (helps ur stun with e skill)

9 Greater Glyph of Celerity
Though useful static ones early game, this is more focused late game, synthesising amazingly well with nashor's at level 18 giving you a ***ping 34% cooldown reduction (9(runes)+25(Nashor's)) it may not seem like much but it will make you able to tank 3 guys easy

3 Greater Quintessence of Potency
I love these quite personally, give you 15 ap, and a little more health in the begining with some nice offensive damage to hit with.

Personally Jax is very squishy early game so how to fix it? simple get defensive masteries, as seen above i get defence, then some health and AP AS increase, then some offensive masteries to amp up his damage output a little more early game

Onto the good stuff Item Build

As Mentioned above it all depends on your current situation.

1. Doran's Shield
I always start with doran's shield, this being simply because it gives defence hp regen and health, wich keeps you alive and fit to keep fighting and farming early game.

2. Ninja Tabi
Right after being able to farm all my gold needed for my boots, i return to base, and voila i got almost a perfect chance for a kill. (explained ahead during skill sequence)

3. Nashor's Tooth
This item has everything jax wants and needs, i always manage to get stinger just before my ulti is ready to skill up, and by that time i got some nice flat attackspeed and i let my ulti do the rest of the damage, if you manage to play it right you should be able to get Fiendish codex and nashor's straight after, giving you the begining of many kills. Also not to mention it manages to fix your small mana pool issues

4.
4.1 Hextech Gunblade
Now here i branched out in case of a situational case, where simply id you need more lifesteal/spell vamp to stay alive, again depending on the situation, i may prefer to get bilgewater cutlass, or maybe hextech revolver. usually i go for bilgewater, simply because it has a Unique abulity to shoot at close range and slow your opponent giving you another kill.
4.2 Guinsoo's Rageblade
This item is amazing, you underestimate it your dead, it synthesis so beautifully with nashor's and your ulti that it's no joke. your attackspeed fully stacked should easily hit the 2.550 mark.

5. Hextech Gunblade
Lifesteal and more Spell vamp, how much more imba can you get? :P

most people start with the leap, i prefer not to for one simple reason, it's cooldown and mana consumption is way too high. and by the time in an early brush fights before a minions even spawn, W has proven to me so much more effective being able to hit much quicker than Q by almost 2 seconds.

W is an amazing skill that has a similar effect to your third hit of your ulti, though both the ulti hit and W do not stack, they can hit consecutivly. Also to note, is it's low mana usage, this makes it perfect for last hitting minions.

Q is a good skill for iniciating, selecting a target in a teamfight, but if im against a squishy i prefer to rush him with ghost smack him up, then finishing with q as he's just about to get away or managed to flash. Also if your gonna harass, use W then Q always helps the damage output

E is an AOE stun amazing in teamfights mostly considering teh reduced cooldown effects where you just spam it over and over, becomming much like kennen in a way locking you opponents in one place, Also this skill is great for farming minions use it all the time :3

R give you magic resist, which is brilliant when it comes to mages, always activate it when fighting an AP char otherwise if it's an AD, don't use it, you never know when it'll come in handy



Skill Sequence in fights:
in solo fights i rush at the enemy with ghost or just run at them, they will underestimate you and attack back, by this time you should be able to run in range use hextech, stun with E, smash with W, stun with E again (if near minions) and continuously spam them with W and E, if they're getting away, o well here i come! Q FTW! and poof there goes whatever remained of their health.

So ...

vs AD
Rush -> W -> E -> (repeat previous two consistantly) -> Q to finish off
Note: Save hextech for if they run, or are low health.

vs AP
R -> W -> Q -> E (if ready) -> W
Note: Save hextech for if they run, low health, crucial moments to kill them off

Teamfights
Rush after the tank, R -> W -> Q (leaping onto thir squishy far ranged squishy Champs) -> E -> W and so on

This Just Depends on your play style what i recommend is

Exhaust (without the upgrade to blind them from the masteries that's just silly)

Ignite (extra AP always helps)

Cleanse (cleans off all those nasty CC's people smack on you

Ghost (awsome for chasing/rushing)

Flash (quickly get in range to Leap, or make a getaway (usually past a wall preferably)

Hextech Gunblade Shot:
Amazing slow effect and effective to KS anytime

Well that's all i got for you this time, this build is amazing if you know your limits of when to iniciate and when to hold back.

All comments on what to use to better the build itself is always appreciated

If you find the need to troll negative things i ask you nicely to refrain from doing so.

Hope this helps!

Enjoy!

Cheerio!