Pros:
-You can build Jax almost any way you want
-He is destructive and a great team fighter
-Pushes lane easily
-Good ganker and ok Jungle
-Easy to get out of Hairy situations
-Get what you pay for (1350 IP OR 585 RP)
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Cons:
-Late game Champion
-Takes a while to get the hang of fully
-Many Champs can counter him
-Wrong build = Under powered

Jax, since he is pretty well rounded champ can make him really easy to build or really tough to build if you don't know what you are going for. Many of you may disagree with this way since there are so many different types of building Jax but personally, by experience, this is the best way to build Jax in 3x3 or 5x5. Give this build a try and you will not be disappointed!

Jax is extremely strong in team fight whether it's getting fed or getting your team fed, Jax will do it. Jax is great at being the first to go in, especially on 3x3's. Right of the start, get boots followed by some potions to keep up your mana and health while getting the Counter-Strike ability. This may sound odd but this is great for face checking the bushes and leading your team in team fights. You will want to use Counter-Strike before running into the bush so by the time it wears off, you are in the bush stunning any enemies that may be lurking within. If you get boots and are the first one to get into the bush you will have stunned any enemies with just enough time for your team to catch up and dominate anyone for first blood. To sum it all up, lead you team and use Counter-Strike's stun before and dodge just before going into hairy situations.

Jax is a hard hitter and almost needs high AD. But, he also relies on a small amount of AP to give you the extra burst of damage you will need later on. That is why it is smart to aim for AD in your masteries but make sure you have enough AP to make a difference at the same time. Armour penetration is also a smart idea especially if you don't see that AP would be useful on Jax. (Might be your personal opinion... Idk...) I would also choose to go with a well rounded amount of magic and physical resist and get back what you are lacking in your actual build. I choose to use demolitionist due not only because of Jax's impressive pushing skills but his passive too. His passive, Relentless Assault, stacks up to 6x gradually increasing per auto-attack granting you +14% attack speed. This enables you to destroy turrets super easily and win lane over-all. Using Empower (W) will make destroy towers faster. That is why it a great idea to use the demolitionist mastery.

It is good to always get all of your abilities to start off. I personally think it is the smartest choice to get Counter-Strike first to stun the squishy start of champs to score fist blood followed by Leap-Strike to leap, stun, destroy, using empower. Other skills can be modified to your liking but I find that upgrading Counter first, empower mid-game and leap last will make your damage counter act the fact that Jax is a late game champion.

Boots of Speed are great for charging and stunning for early first blood. The extra starting gold can be used for potions of your liking. I recommend 2 health potions and 1 mana potion. If you hold your lane well enough, by the time you need to recall you should be able to get Ninja Tabi to help make you tankier and faster. I then recommend that you start your build for trinity force. Start with Sheen. Sheen gives you and extra needed boost of ability power and more mana to help you stay in lane longer. Jax is kind of a mana sucker and starts with really low so get sheen first when you build trinity. Now that you have the mana that you need, aim to get more health and armour by getting yourself Frozen Mallet. With Ninja Tabi, you will have enough speed to close the distance on your enemies but you might notice that they slip away sometimes. Frozen Mallet with counter this! Use counter to stun and auto-attack the enemy champ to use frozen mallet's passive to slow their movement speed. Continue your Trinity Force build by getting Zeal next for extra speed and AS then finish it off with Phage for health and AD. Now purchase Trinity for 300 and it will upgrade you in almost every stat that Jax needs. Now, what if your enemy turns around on you? You will need Frozen Heart to give yourself the extra armour and health, slowing their AS with it's passive! Now they can't get away and can't stay and fight! The next 2 items are optional but I highly recommend Blood Thirster for the AD and life steal you need along with making their job harder by giving them return damage on an already tanky Jax. This build may be expensive and you may not finish it fully but it is the strongest build for a tanky bruiser Jax that I have used.