Hello and welcome to my first build guide! For this build we will be focusing on Jax, the Grandmaster at Arms. One of the first things I'd like to discuss before you read any further is you will have a slow start due to the dodge runes and balanced mastery tree. First blood is possible by combining your Exhaust and Ignite with your Leap Strike.

For runes I chose -

Seals: Greater seals of evasion with a 0.75% dodge chance.
Marks: Greater marks of alacrity with 1.7% attack speed.
Glyphs: Greater glyphs of alacrity with 0.64% attack speed.
Quintessences: Greater quintessences of evasion with 1.5% dodge chance.

The reason I have my runes set up like this is for 2 things: The attack speed is extremely helpful early game and also mid game. It will help secure that 3rd hit from your ultimate when chasing a champion. Flat attack damage isn't as helpful as that can be completely substituted with items. The quintessences and seals are my favorite part, Dodge chance. Without dodge Jax can be an extremely squishy and vulnerable champion. Dodge will help you evade attacks and take little damage early game, and late game helps extremely with your E, Counter strike.

For masteries I've decided to do an even 10/10/10 split. This allows you to have a bit of each mastery tree, gaining the most helpful masteries such as Burning Embers in offensive, Nimbleness in defensive, and Meditation in utility.

Offensive:
For the offensive tree you really want Burning Embers for your Ignite and Archaic Knowledge's magic penetration is always useful. You also get Cripple, which compliments your Exhaust, making them even more vulnerable to your AP/AD abilities.

Defensive:
The #1 reason you go in the defensive tree is for Nimbleness. This has saved me countless times when I've been ganked or outnumbered. After dodging a couple of attacks your Counter strike will be ready to cast. After you stun the attackers your Nimbleness will kick in giving you that 10% movement speed, getting you safely out of the one-way fight.

Utility:
The reason for the Utility tree is for Awareness and Perseverance. The Awareness will help you outlevel your enemies in your lane, making you to be quite a threat. The Perseverance is also helpful to be maxed out as it gives the health regeneration and mana regeneration. Two things that can only benefit Jax.

My personal preference for Jax's items are on-hit effects. Lichbane/Sheen's passive is extremely helpful with Jax as you can Empower, Leap-Strike, then auto attack, giving you an extremely effective and brutal burst.

Ninja Tabi
Almost self-explanatory. The 12% Dodge chance is a must with all Jax builds. It benefits your E greatly and nothing's wrong with dodging an attack. I always take my Boots of Speed first with 3 Health potions and then go back at level 6 and buy the item completely. I usually have enough gold to start on my Hextech Gunblade as well, picking up a Vampiric Scepter.

Hextech Gunblade
This is my favorite and core item for Jax. I always start with the Lifesteal as it helps laning. Need some health? Go club some minions. After finishing a few minion waves or a tower or champion I recall and purchase the Hextech Revolver, giving me some spellvamp and Ability power, making my moves that much more deadly. At this point Jax should be undefeatable in 1 on 1, as long as there's little CC present. If the enemy is escaping and your leap is on cooldown, use the Unique Active of the Gunblade and secure that kill.

Guinsoo's Rageblade
This is my second favorite item for Jax. It's like a mini-ultimate. It adds some relatively high Attack Power and Ability Power, giving you that nice 50/50 split Jax uses so well. The passive gives you 4% Attack Speed and 6 Ability Power per stack, stacking up to 8 times. This combo'd with your ultimate's passive should give you some hilarious attack speed when focused on a champion or tower.

Sheen/Lichbane
This is my alternative to Phantom Dancer builds. Although the attack speed is very nice, your ultimate and Guinsoo's Rageblade should cover for you. I loved Phantom Dancer until the dodge chance was removed, making it nearly useless for Jax. Lichbane however gives you that great on-hit effect I was talking about earlier. After using an ability your next attack is going to shred the enemy. Your ability power determines the extra damage dealt, which is why this build has so much dependence on it. The movement speed is also welcome for Jax, along with the extra mana.

Rylai's Crystal Scepter
As of my 5th item the match is usually finished in my favor but if it's a very neck in neck game then I usually start adding some more ability power and attack damage. The reason for this item is the 25% slow. Besides his stun, Jax has no CC and can allow some champions escape if tanky enough. This is where Rylai's comes in. When you do your empower leap-strike combo you should have slowed them down, and if they fight back you can stun them as well, rendering them slow and easy to kill. The giant's belt is also favorable as there's nothing wrong with having more health.

The Bloodthirster
My final item is Bloodthirster. When I'm starting to work on a 6th item I'm usually doing something wrong that match and go for some more Attack Damage and Lifesteal. That's all there is to it. This paired with your Gunblade's lifesteal and spellvamp should keep you at 3/4 health or above.

My skill sequence to Jax is the same as most other builds. You want to level your Empower first, as it does a large chunk of your damage and has a relatively low cooldown. You also want to take your ultimate whenever possible. When you're done maxing Empower start working on Counter strike as the passive's dodge chance is a lifesaver. Save Leap strike for last as it does not do as much damage as empower and has a long cooldown.

For my summoner spells I almost always go with Exhaust and Ignite.

Exhaust:
Exhaust is just all around helpful. It allows you to slow a target down to get that final hit on them or to get them in range of leap-strike, or it can be used defensively if you're being chased. With the mastery point their magic resistance should be shredded so you can dive in on them, proving them to be an easy fight.

Ignite:
Ignite is also helpful as it allows you to get that last bit of damage on them when they're running. Although your Hextech Gunblade fills this position mid-game, this is still a helpful summoner spell to take. The mastery point gives you that extra 10 Ability Power whenever it's on cooldown, so it's a win-win either way.

Other Options:

Other options I recommend would be Flash for escaping through walls or catching up, Ghost for the same reason, or Cleanse to take care of any CC they put on you.

Final comments I have on this guide regard Jax's playing style. Jax can be played various ways but is most effective when his abilities are taken advantage of, mainly his dodge chance and stun. Jax's stun allows him to initiate a fight and escape mostly unscratched, while his leap-strike and empower make great tools for harassing. His ultimate's passive is also effective when focusing on a target for long periods of time. When under fire you can always activate his ultimate giving a nice Armor and Magic Resist shield.

Any questions you'd like answered, go ahead and comment. Thank you for reading my guide and be sure to comment if you have another method or suggestion for me to edit in. Thanks!