Jax is a fun champ that can thug against almost any kind of team he's facing. There is a learning curve, but it's not a very steep one, and it mostly consists of figuring out what shenanigans you can get away with.

You can build Jax a lot of different ways, so the aim of this guide is not to bring down any stone tablets from the mount, but to provide you with some flexible guidelines and suggestions, so you can fit this champ into your playstyle.

So, broadly, the stats that you're looking to make use of with Jax are:
Dodge
Attack Speed

From there you can decide what you value more:
Ability Power
Attack Damage

Leap Strike - In almost any fight, this is going to be the first ability you use. Picking up a point in this skill at the start of the game makes getting that First Blood a lot easier. The cool down, especially early on, for this ability is just a little too long (you could try to mitigate that with runes), so plan accordingly.


Empower - This is your bread-and-butter spell. It has a low cool down and hits hard. Max this one out first. Be sure always to cast this before you use Leap Strike or otherwise engage in combat. However, once you have Lich Bane, remember that the item's damage boost has a 3 second cool-down. Leap Strike will proc the LB boost, meaning that it's better to wait 3 seconds after you initiate before popping Empower (to get the boosted damage again) rather than just spamming all your abilities immediately. Of course, sometimes you don't have 3 seconds to wait.


Counter Strike - This move is awesome. There's no other way to put it. Always pay attention to when this procs, as it can turn a bad fight into a good one. But don't get so caught up in watching for this move to become available that you lose sight of more important things like your health. Even without the dodge chance from old Phantom Dancers, this move still procs a lot, and can allow you to easily win 2-on-1 fights even at low levels. It procs more frequently the more points you invest in it, so I like to max it out second. However, if no one on the other team relies on auto-attacks, I'd recommend only getting one point in this at level 4 or 8, maxing out Leap Strike second instead, and building AP.

As an added bonus, this is also a really good farming spell, and it will allow you to build up fat creep waves.


Relentless Assault - This is why Jax is a monster. It's not an ability you really have to think to much about. Just let the passive effects make you a killing machine, and pop the active when you start getting cooked.

Exhaust - I think this is a must-have for pretty much any and all melee DPS'rs. It's going to allow you to chase more effectively, take less damage, and by being specced into it, dish significantly more damage out.


Flash - I flip-flopped a lot between this spell and Ghost, and I can't say definitively which one I really think is better. But, I like Flash because Jax seems to overextend himself (just by the mechanics of Leap Strike) constantly, and since he can't take as much as he can dish out, I like being able to instantly get out of harm's way rather than trying to outrun opponents.
I do miss the sustained chases that Ghost enables, but Flash will let you hang around bad fights just long enough to get a kill before blinking out of harm's way with basically no health left.

With that said, I think these are the best alternative spells:



Ghost-chasing, escaping, baiting, crossing the map; this is a versatile skill that works successfully on almost every champ.
Cleanse - There's no room for Mercury's Treads in this, or really any, Jax build, so Cleanse can be a real life-saver

Ignite, Heal, Teleport, and Clairvoyance are all viable, if those are the spells you are accustomed to using.

RUNES:
ArPen or MagPen Marks? I'm not entirely sure myself, and I'd like to hear your opinion. I ultimately opted for MagPen because this will aid your abilities (again mitigating the low AP of the build) as well as boosting the damage from your Sword of the Divine and Madred's Bloodrazor. Furthermore, with Sword of the Divine and The Black Cleaver, you'll counter armor fairly well as it is.

Dodge Seals are a no-brainer.

Since the items now provide very little AP, Ability Power Glyphs mitigate the way in which AS/AD builds minimize the strength of your abilities. And if you build AP, a little more of the stuff couldn't hurt.


MASTERIES:
Not a lot that's too surprising here. I sacrifice a little crit/attack damage to get the magic pen that will boost your Ultimate, Leap Strike, and Counter Strike.

Why did I only list 4 items at the top of the build?

Like I mentioned, Jax is a very flexible build champ, and I feel that only 4 items are necessary. And, in truth, even those aren't set in stone. The way I see it, for the first 4 items you want items that give you Attack Speed as well as damage of some sort (whether it be physical or magic). These 4 just happen to be the items within those criteria that I like best.

CORE ITEMS


Missing Mercury's Treads is a bummer, but since a lot of your effectiveness depends on Counter Strike proccing, you need all the dodge you can get, especially now that Ninja Tabi is the only item in the game that grants dodge chance.

With the other three core items, the goal is achieving absurd attack speed. with just these 4 items at level 18, you'll have 270% AS after 10 attacks. We might regret losing the AP that would make your ultimate's procs hit harder, but this madcap AS means that said ultimate will be proccing much more often, dealing equitable (if not greater) damage.
Think of it this way, if we assume our target has 2000 HP, every hit you'll be dealing 80 bonus magic damage. Every third hit, you'll be dealing 374 bonus damage; every fourth hit, 180 bonus damage. But every 12th attack you deal 474 bonus damage--ouch! Talk about a relentless assault indeed.

Guinsoo's gives us some nice AP and AD in addition to the attack speed, which we desperately need as fast as possible after the Sword.

Sword of the Divine gives us monster AS and some bonus damage, but the item's active provides much needed ArPen, and can be invaluable if you ever have to go toe-to-toe with another Jax.

Despite being "core items" I find that many games you'll want to trade out your Madred's for a different item. Here are my top two replacement picks:


This is a great item for Jax, and can move your build in the AP direction if you start noticing a lot of armor going up (or if you see from the very beginning that you'll have to deal with Malphite or Garen, etc.). I'd recommend ending the build out with Rabadon's Deathcap and Lich Bane if you pick this up.


Awesome anti-caster item. I always choose this if there are no opposing tanks (or Rylai's/Rod of Ages casters). However, I'm always hesitant to pick it up if even one of my opponents doesn't use mana. As a bonus, this item is far cheaper than Madred's, so you can move onto the rest of your build much quicker.

It's up to you to decide how to finish out the last two items. I would suggest however, choosing one of 3 avenues:
1. AD and Survivability
2. Crit and AD
3. AP

1.
I like these two items a lot. The Black Cleaver helps you further counter enemy tanks, while boosting your AS to 300% and giving you a nice AD bonus. As for the Bloodthirster, late in the game (or even early in the game) Lifesteal can make a huge difference. This item is a quick and easy way to get a bunch of Lifesteal.


This is a viable alternative to The BC if your opponents take Armor to a maddening level (I think this gels with Sword of the Divine's active, too).
**DO NOT BUY THIS ITEM WITH BLACK CLEAVER** Because it operates on a percentage of the target's armor, BC, as it removes armor, will actually make this item less effective.

However, if you don't really have to deal with tanks, there are plenty of other items to choose from.

With insane AS, this item makes you a terror in team fights, basically sending out an incessant wave of extra damage to every opponent. Plus, you get some health and mana regen, which is nice.

I don't really like this item on Jax, but it will ensure that no opponents escape you. Never ever. The HP is a nice bonus, too.

This is also where you would end your build with defensive items such as:


2.
Ending your build in this way, will get you a nice movement speed bonus. But more importantly, you'll get even more AS (you'll be at about 315%) and a load of Crit and AD. While these two items alone will only net you a less than impressive Crit Chance of 50%--%60 with Jax's base stats--but at hypersonic attack speeds, that chance will be more than enough.


This item has everything Melee DPS'rs want: AD, Crit, ArPen, and with its active, AS and Movement Speed as well. However, I think that it will stretch your stats out too thin to be as effective as the blunt bonuses of PD and IE.

3.
So, technically this is really hybrid more than AP, but I like hybrid items on Jax much more than pure AP ones. Jax takes huge advantage of both lifesteal and spellvamp, so the Gunblade is a perfect fit. Furthermore, hybrid items don't squeeze Jax like they do other champs because the spell he relies on most, Empower, utilizes both AP and AD. This means that Empower will get a bonus of 40 from Gunblade and 24 from Trinity Force (as opposed to 22 and 12)
Trinity Force is also an awesome item, not simply because it gives you a little bit of everything you love, but also because you can pick up one of its relatively cheap components early on in the game if you see fit. I'm wont to grab Sheen, for example, long before I have any intention of completing TF.

However, because hybrid items don't really provide staggering bonuses for your spells (nor your ultimate's procs), you may feel it's worth it just to boost their damage a great deal, being as you have such a high AS.

These are powerful items, and any combination of two of these will allow you to pump out magic damage, which can be incredibly useful if your 4 core items fool enemy tanks into stacking armor.


Monster AP item. If you feel that you've got the Ability Power to make the 30% boost worth it, I highly recommend it. Could be devastating if you bring in enough cash to buy it in conjunction with Lich Bane.


These are solid AP items that will provide some defense as well.

So, in sum here are the complete builds that I would make with Jax:








I don't advocate:

Late game wipes hurt your team enough, without suddenly seeing your effectiveness plummet by a third. They also make you play much more selfishly, more reluctant to push, and all around pull you away from thinking of the game as composed of two 5-man teams. And really, if you're playing against anyone at your skill level, they shouldn't allow you to get very many stacks anyway.

Starting Item

I have come to like Doran's Shield the most out of all the possible starting items, as it has many a time allowed me to get first blood when I should have became first blood.
Doran's ring is an awesome alternative, though, which I will generally take if I see my opponents will have more HP than DPS at the outset of the round.
Boots are nice to start, allow you to chase and get FB as well as make Leap Strike harassment safer because you're faster than everyone else. Plus, having 3 health potions instead of one is always nice.

PLAYING AS JAX

Early Game
The laning phase is pretty simple. Harass heavily with your Leap Strike/Empower combo. Don't tower dive unless Leap Strike, or preferably Flash, is off CD and you know you'll be able to use it to jump to your partner or minions outside of the turret's range.
If you picked Ghost, you can do some pretty sick drive-by's, if they have low health, and still survive. I wouldn't recommend it on your first few games with this champ, though.

Also, start trying to get a feel for how much burst you can do with Leap Strike and Empower. Most people will be reluctant to recall from their lane and lose XP, lingering around with low health, and many people underestimate Jax's range, so you can oftentimes pick off an easy kill even if it looks like you're diving headfirst into a 1v2.

Mid Game
This is when you can start roaming and ganking--assuming your lane is stalemated. Leap Strike has good range, and you, coupled with some teammates, can really roll over-extended enemy champs. However, at the end of the day, your real mission is to push down the opposing tower in your lane, so prioritize that over ganks.

At this point, minor team fights of 3 or so per side have probably broken out. This is when you can do some goofy stuff as Jax is a really good baiter. For example, if you see a couple of enemy champs, get your team set up nearby in the jungle somewhere. Leap Strike in and burst the squishiest opponent with Empower. Pop Relentless Assault and get ready to run (you might even have time to kill said squishy, but don't count on it). You'll probably be losing a lot of health, but you should have aggravated them enough to the point where they'll give in, and you can just waltz into your team. This is a good way to not only feed your peers, but also go for some really silly and embarrassing kills yourself. Don't get too cocky with this sort of thing, though, and forget about CC because you'll end up dead, looking very foolish.

Late Game
To me Late Game means whenever the big team fights start.
It's important to remember that while Jax is fairly tough, he's not a tank, and he will get torn apart if he gets caught out. Jax, however, is very effective at targeting and working down more fragile carries, as he can just jump over the tanks out front. Let someone else on your team initiate, and then go to town with Leap Strike/Empower (and hopefully Counter Strike) on said carries.

Something else to remember is that enemy creeps are sometimes your best friends. They're easier to dodge than champions, so you can use them to proc Counter Strike. While it's up, Empower up, Leap Strike into the enemy team, and stun all of them with Counter Strike. Your team should be close behind, and should be able to take serious advantage of the momentary group-stun. Be sure that you communicate well when doing this sort of thing, so that your team is ready. Also, always know your escape route ahead of time, as the idea is to get in, get out, and then get back in once they've started targeting somebody else.

During the downtime, be sure to grab the Red Buff as often as possible, as the slow will help you immensely. Blue Buff is something of a non-priority for you, as you rarely have mana worries. If no one else on your team is picking it up, you may as well grab it. Also, don't forget that Jax is a strong farmer. Use this during downtime to make serious cash, and build up big creep waves. They'll stretch the other team out, and can possibly work down some towers, too. These waves can really turn the tides of long, stalemated games.

In summary, Jax is one of the most dynamic champs in the game, so use that to your advantage to be everywhere in fights and on the map. Most of all, play like crazy and I think you'll find him rapidly becoming one of your favorite characters.