Simply put, it's the best build I could possibly muster up for Jax on TT. If you can manage to complete it you're anti-anything-that-uses-aa-to-attack. This goes for everything up to and including tanks. We all know Jax is one hell of a carry, but I've yet to see anyone build him this well.

I made sure to include summoner spells to help you out in a pinch, and starting gear to help you stay in a lane longer before having to retreat. It's especially useful against anything that relies on poking to get you to leave. I am aware that my guide doesn't work in all situations (aside from the general order of the building).

I made sure to include enough sources of passive and active damage to stop you from being countered easily, and enough cooldown to make sure you can fire off your now lethal abilities as often as possible.

Overall, this is meant to maximize all of Jax's offensive capabilities - giving him tools to deal with most, if not all, situations- and at the same time minimize the amount of time he would spend out of battle for items, health and mana.

Now I'm sure you're questioning the sanity of filling a entire page with a single type of rune. The thing is, this works to your advantage when you consider the starting items I recommend. You effectively start off with a recurve bow before spending any money, have enough lifesteal to avoid dying from light to moderate pokes and spending money of single-use potions; and a boost in run speed so you don't spend too much time away from the action if you need to recall.

It's a straightforward rune setup meant to overpower those who haven't specialized in defense right off the bat.

So most of the offensive masteries are self-explanatory. There are a few I would like to bring your attention to though. Note the cooldown reduction, magic penetration, and lifesteal. Normally I wouldn't recommend these for any character that doesn't already specialize in one of those, but Jax is an exception. The entire setup relies on these tiny bonuses to give you an edge throughout the game with no drop-off point on anything.

The otherwise insignificant lifesteal now gives you a 20% boost on your newly purchased vampiric scepter, the cooldown reduction brings your score right up to the cap in the mid game, allowing you to fire off your abilities often and as such further improve your healing factor, and the magic penetration works in sync with the BotRK (more on this later). I would not suggest using those points on anything else.

Here we come to the central piece of this guide. No doubt the first thing you looked at was the item layout. The most interesting piece, I think, is the BotRK; the first item you actually build into. "Why?" you ask. It's simple. This lets you begin punishing those who stack health (which nearly everyone does) while granting you both active and passive sources of health at once. Furthermore, you can steal your fleeing opponent's speed to close in for the kill. Another alternative to have is either the Bloodthirster, or the Sanguine blade. They can both be quite appropriate if your opponent isn't actively stacking health.

After this, I emphasise cooldown reduction, movement, and attack speed to capitalize both on Jax's passive, and your item's at once. Once you finish maximizing these aspects, one can focus on broadening their options when it comes to slows, damage, and survivability. For that I recommend you buy the items as they appear on the list (of course). First you start off with the gunblade to boost the damage done by your attack and your Ultimate's passive; while at the same time boosting the armor and MR bonuses your Ultimate's active effects grant you (among other things). Then you can begin to focus on the trinity force for all its benefits (at a time you can both guarantee you'll use every last one of it's bonuses to their fullest, and where getting the gold for it isn't a burden).

By this point gold farming should be a piece of cake. It shouldn't take you more than five minutes to get the gold needed for this item. Last but not least, you can finally afford to get the Infinity edge. It has only one bonus aside from its stats, and that's the boost in critical damage (which is also improved by one of your masteries).

Right at the start, you'll want to get counter strike. There's no point in getting leap if you'll be jumping to your doom, and empowered strike requires you to be within smacking range before you can hit with it. I suggest you focus almost exclusively on leveling counter strike to be able to dodge opponent's auto-attacks and stun them more often. After that, empowered strike should be your priority. The cooldown ends up being exceptionally low; perfect for dealing damage to your potential target. Then last but not least, leap strike.

Needless to say- if you can level your ultimate, do so immediately.

Pros:
1. Variety: You deal all forms of damage and are left with a wide variety of spells and debuffs to deal with several opponents, or a single persistent one.
2. Efficiency: One spends more time fighting on the map and less time dead/recalling.
3. Burst: You deal obscene amounts of damage to all. This includes the otherwise untouchable "tanks."

Cons:
Survivability: You have access to sizable armor and MR boosts for a few seconds at a time after cooldown. This works better in guerilla style gameplay than it would in all out blitzkrieg. With a concerted team effort, one can be killed relatively easily (emphasis on "can"); your boosts simply being waited out by cautious opponents.

Here you're going to want to avoid getting into extended conflicts. Just focus on isolating and stunning targets to get a few kills in before the minion spawn. If you're successful, you'll be able to purchase the Ionian boots of lucidity (Or save up for the BotRK). Make sure to keep a support (preferably one that heals) near you at all times. Around level 3, you should be able to zone your opponents out with a quick E,Q,W combo; allowing you to farm with fewer worries. I wouldn't recommend trying that with more than one enemy champion present for now.

Just make sure to focus on farming and don't go back unless you absolutely have to (say to buy items, or restore mana if you don't have Soraka as support and your clarity in on CD). Also make sure to keep a few wards deployed so you can leap to them in emergencies.

When you finally have your first three items, you are prepared to start making some real progress. Roam the map and ambush lone targets while pushing objectives. You should be able to get a kill or two on your own before needing assistance. At this point, I would suggest you make it a point to capture all the altars (if you can). It should put pressure on the enemy team to leave the lanes, allowing your teammates to farm more easily.

By this point you should also be able to kill Vilemaw on your own. Doing so would grant you a significant boost to your health and mana regeneration, plus an attack speed boost and additional cooldown reduction (though you likely won't need it at this point).

Here is where you excel. At this point my best advice to you is to cast a slow of some sort on your opponent (you'll have several at this point) and close in with the E,Q,W combo. The ideal strategy is to force an Ace then destroy the towers. But this isn't always viable. If you find that your opponents are killing you too quickly, I suggest you switch out the Infinity Edge for a Guardian Angel. That'll help you live a bit longer by both synergizing with your Ult's active effect and by reviving you if you die.

Another option is to use the Force of Nature if most of the damage you take is magical in nature. It helps you survive against magic attacks better by both reducing the damage you take from them, and by boosting your health regeneration rate.