Well hey yall. The first thing I'd like to clarify 'bout this guide is that it is designed for playing Jax Mid. What's important to keep in mind is that, like most mid champs, he is better against certain champs, and worse against others; however he is overall a very strong pick. I have played champs like Shaco Mid before, and while I usually do well, I know that that isn't viable. Jax Mid is the real deal, no troll stuff. Well, this here is my first guide, as most of these guides seem to be, so this is my joining the fray, I hope yall can give some good feedback on how I should edit the guide, and maybe even try it out and tell me how it went for ya! :D

Disclaimer: This guide is not intended to be used for blind pick

For my Marks and Quintessences I like to take Armor Penetration because, hey, you're mid, git some burst! Leap Strike and Counter Strike both deal physical damage, so armor penetration gives both of these a nice little (Big Actually, about 20%) boost, in my opinion better than pure physical damage would, and of course Armor Penetration will help out in those famous Jax Smashing Sessions (AKA Autoattacking). For Glyphs I take Flat Magic Resistance because they are the best. When you make those exchanges with the enemy mid you will take much less damage than they will. This is a good thing and indisputable. Other runes here are just silly and not really good at all ever. For seals I take armor per level because seals are for defense or gp/5. I don't want magic resistance here because it doesn't really scale well on seals, I don't want gp/5 because I'm not a support, and I don't want flat armor because they deal magic damage in lane anyways, and getting armor per level will help me out later.

The 21/9/0 Masteries provided are what I prefer, but these could be changed depending on player preference and the situation. Three points in Vampirism and one point in Executioner are Mandatory for this guide.

I find this item build to be extremely effective; however, items can be switched in the order or entirely replaced when the game requires it, as items should not be one set path. Buying two Doran's Blades work in combination with Vampirism to give you 9% Lifesteal, which helps tremendously and is a vital part of this guide. Boots are important and should be bought soon in the game. Mercury Treads give you tenacity too keep you pursuing your target, and supply magic resistance to help mitigate the damage from the enemy's burst. Sheen will help with your own burst, and allows you the option to either Empower, Leap, Attack, or to Leap, Attack, Empower, Attack. Rageblade is necessary for getting Brawling Stats that Jax is so famous for. Trinity Force helps with everything on Jax and is overall a great item. These last three items are all very good and can be built in whatever order you so choose. Guardian Angel gives you the ability to facedive into a 1v3 to git you sum feed. It also allows you to be an extremely threatening force in team fights that will put out damage and never die. Gunblade provides even further chasing power as well as strong sustain in fights, on top of that extra damage. Warmog's makes your ult that much better, and is often better to get after your Guardian Angel.

Maxing Leap Strike first is MANDATORY. This will lower it's cooldown to help you always be able to escape ganks and to zone the enemy with the constant threat of being pounced on like a Large Housecat on Tuna. The damage boost essential for that bursty mid type playstyle. I highly encourage maximizing Empower second, as you can add its damage to your Leap Burst, and just turning it on may send them running in fear. (Of course max your R first)

I take Flash and Ignite, as they make for an incredible threat of a long range Burst Kill, both within your lane, and when you Gank. The only others spells that I could see taking are Exhaust and Teleport. If you take other spells then you are silly (including Surge).

Counter picking with Jax is very important, as with all mid champs, but not many people know what he does well against, and what he fails against. I will provide a list

What Jax Kills:

Champs with a strong reliance on AOE damage. You can safely stand in the middle of the wave last hitting, and know that if they use their AOE they will help push your lane back, allowing you to Autoattack their minions more, building stacks on your passive and gaining health back because of your Lifesteal.
Champs that use AOE generally use skillshots with projectile speed. The slower this projectile speed is, the better Jax can pown them on their faces. When the enemy heads in your direction to engage you, be prepared. When they begin their cast animation you leap to them, often avoiding their combo while being able to fully enact yours. For first target type skill shots you should be mostly unaffected because you are sitting in the middle of all your creeps.

What Kills Jax:

Large Health pools and Defense.
An easy to land Stun or Snare.
Champs who can flash or dart away will just do this when you jump on then unless you're very good with your stun
(Avoid Morg, Sion, Ryze, Ahri, Ezreal, Vladimir)

Pros:

You have great survive and early game burst
It should be easy to zone your enemy
Your Ganks are awesome
You have great late game survive and burst, as well as sustain
People will not think you are mid and most likely will not counter you
If they accidentally counter you you can still switch somebody, where they (or you) will take Jax top or jungle, and you (or they) will counter their mid
You can jump on people
Jax is OP
Anivia walls are awesomely useless

Cons:

You are ineffective if you are countered
You are an AD mid and require either AP top or AP jungle
People may troll you when you try to pick this (For Now)