Welcome to my in depth guide about Kennen.
I've uploaded it before even half is done, but this is because people were aking me a lot about my AP Kennen build, tips n tricks, etc. So one build I finished, the others I am working on, but don't expect any rapid progress, 'cause I'm having exams soon ;)

I have tried numerous builds for Kennen, good ones, bad ones. I've tried a lot, but not all, and therefore this build is still in progress. Here I sum up the possible kinds of Kennen that there are to be found:
-AP Kennen
-AD/AS Kennen
-Hybrid Kennen
-Halftank Kennen
-Fulltank Kennen

Personally I play AP Kennen, with a build that most people find rather strange. As I know this I hope you guys will not hate even more, but only say something once you've tried a build. I will explain in detail everything about my builds and strategies.

I warn you also: Kennen is NOT an easy champion, or rather: my build is NOT easy to play. So be warned, he is extremely squishy and I have no support from runes or masteries either. My tank and halftank have a lot of health, though and the AD and hybrid have life steal and/or spell vamp. Those are thus easier to play.

Still bear in mind that when you master the AP build it will result in much higher scores and much more damage output. This, however, is not easy and will take some practise and time.

I decided to start off with the Skills.
Kennen has 4 skills, of which one ultimate, like most champions.

1: Thundering Shuriken. (TS)
This has amazing range, hits generally high and is quite easy to aim. You will need to try it a few times, but after a while you should be able to harass easily with it. After you've landed one on a champion you should try to hit Electrical Surge as fast as possible.

2: Electrical Surge. (ES)
This is when Kennen starts to shine. His passive gives a Mark of the Storm every 5th attack. Personally I auto attack minions untill I have Electrical Surge's passive ready. Then I auto attack on my opposing champion (no aiming required, since it's not a skillshot) and right after that I hit Electrical Surge causing more damage. This is a very effective way to harass.

3: Lightning Rush. (LR)
This skill is very useful to move around with and get out of sticky situations, but the cost is pretty high, which is why I upgrade it last. (Excluding my defensive builds) Also it doesn't do as much damage as the other two skills. This is really an endgame skill, to easily land Marks of the Storm on a group of enemies when they are in a teamfight. After this you can do Electrical Surge again to hit them all again.

4: Slicing Maelstorm. (SM)
This is Kennen's real pride! This skill does amazing damage per 0.5/0.4/0.3 seconds (depending on its lvl) and it hits a lot of Marks of the Storm on enemy champions (Up to 3; so at least one stun over 5 sec. > 5 champs > 0.9 sec per stun > 5/0.9~=1, so every champion once). This way they get stunned quite easily. Yes it truly is an ultimate ^^ nevertheless it is only strong if used in a proper way.


I start off with TS, which I use to harass with straight from the beginning and usually we try a first blood gank where it is nice to have someone extra with range.
After TS I take ES because of its passive mainly. It now is already possible and even quite easy to stun enemy champions. By auto attacking minions your passive grows until it has 4 stacks. The 5th attack is the important one. (Under in your screen the picture won't have 4 in it, but is blue, meaning charged. You can also notice this by seeing the electric glow on your shuriken and the fact that if you hit your shuriken is blue in stead of yellow.) Now you don't hit anymore for a little while, causing your opponent to push a bit. Once he is close enough you hit him with auto attack. He will now have his first Mark of the Storm (MS). Now use ES to damage him and add another MS. Now there are some options. Either he goes behind minions and you await your next chance. No time wasted though, 'cause you've damaged him. If he goes for the fight stun him with your TS and kill him. (Remember: use ignite!) If he runs it's even easier. He will run past minions and in the open you hit him with TS to stun. Now use auto attack and ignite to finish him. If he manages to run further just take him out with your TS.

Well after this I take LR to make it easier getting away, chasing enemies, placing MS on targets, running through the map, what not.

First I focus on lvling up TS, because it's your main source of damage and the best way to harass. After this I lvl up ES, because it makes it a lot easier to chase champions in general, plus it makes harassing and pushing better/easier aswell.
I save LR for the last, because you'll need it more at the end when people hit you harder. Then the extra defense and magic resist bonus is useful.

However... With the tank build I upgrade LR first, because of it's passive that gives you the extra magic resist and armour. This grows by 10 every lvl and makes you very hard to kill in earlygame teamfights. You rush in with LR and use ulti to stun. You'll have high defense and magic resist for a short while, even after LR expired and thus you will tank your team longer. The opponents will focus you, because of your ulti, but this is good, since you are the tank.

This is the most obvious of all builds for Kennen. All his skills use AP, so get a lot of it and you'll hit high. Easy: yes? / no?
Well.. not really.
Kennen is a seriously squishy champion and in this goes even more for my build. I do not use Zhonya's Hourglass and neither do I use Relai's Scepter. I will show you why and I will explain why this build is better, and how I manage to win against every other Kennen that I've met so far, who is using just those two items.(or one of them)


Runes:
My runes are a little obvious, they seem to be the best for Kennen, so..
-Marks with Magic Penetration
-Seals with flat Ability Power
-Glyphs with Ability Power per lvl
-Quintessences with flat Ability Power

I currently found out there are Seals with Energy Regain per lvl, and so I will try to save for those to try it out. This will be 10,30 for 9 Seals on lvl 18, which is a lot.
I do not use the Cooltime Reduction Glyphs, because I feel there isn't a need for them. 5% off your ulti's Cooltime would be nice of course, but 28 AP on lvl 18 (+30% from Rabadon's) makes a good alternative. I chose the AP per lvl in the end, because it's not every game that you get feeded, and so it's nice to always have the AP you would like.
As for Quintessences: I guess you could use the HP ones, but really the 15 AP from start is kind of great, so I wouldn't recommend it. Also taking AP quints per lvl are relatively useless, because you only gain 2x3=6 AP from doing that. And having 6 AP more or less in the end doesn't matter too much, while having 3 AP or 15 AP at start does matter a lot.


Items.
I'm not going to repeat what is above already, but I will tell you why I chose certain items over others. I've recently had a lot of questions, why this, why that? blablabla..
-Why don't you take Mejai's Soulstealer as your first item?
Because I find it difficult to get stacks fast without having some Magic Resistance. You often get focused down, and it's a shame to buy something that gives such low AP when you die all the time. If you feel like a pro, be my guest and buy it, but believe me if I say that getting 20 stacks is still possible (and quite a lot easier) when you have Abbysal Scepter.
-Why don't you use Relai's Scepter?
Because it only gives 15% chance on hit to slow on multitarget spells and Kennen has 4 skils of which 3 are multitarget. Therefore I find the chance to hit to slow too low to be useful. The 500 Health is great, I cannot deny that, but I feel that it's not nessecary if you know how to play Kennen. I admit it will make the gameplay somewhat harder, but getting other items instead will boost your damage and that's what Kennen AP is all about. Damage and nuking.
-Why don't you use Spell Vamp?
Same reason as Relai's Scepter. I feel like you don't really need it. The items with spell vamp are expensive and they give some AP, but not a lot. The active from the gunblade is nice, but Kennen should be used for teamfights, and killing 1 person with ur "epic active" isn't really the way. Better focus on flat AP and Magic Penetration to make sure you kill all people in the teamfight, rather than one. (Besides the passive from Lich Bane is already focused on 1 person, that should be enough in my opinion)
-Why do you wait so long with buying boots?
This is my personal preference. You can buy the boots first, but I think the Abbysal Scepter is more important. It gives magic penetration aswell as AP, so it increases your damage much more than the Sourcerer's Boots. (Yes it is more expensive.)
Another reason for this is that you can always run through the map using LR, meaning you run fast anyway so you don't need the extra speed from Sourcerer's Boots if you just use Kennen's skills in a proper way.

Then the next problem is Zhonya. Should or shouldn't you take it?
I used to get it always, for it's amazing active. However, then I realised you don't really need it. This again will make Kennen's gameplay harder and him more squishy, but it is pretty doable living without the Zhonya. If you feel like you are too squishy or you are having problems endgame because they focus you down all the time I suggest to take the Zhonya's Hourglass after your Rabadon's Deathcap and then skip Lich Bane. This, because you can't hit while being in Zhonya's 'buff' so there's no need for auto attack passives, while for instance Void Staff will still do it's work on your ulti.
A second option is waiting untill you have all the items and selling Mejai's Soulstealer. (Because if you get focused down a lot you will have a hard time building the stacks. Therefore it won't be so great as it normally is and it might be better to have something with 100 flat AP and some defensive abilities; Zhonya's Hourglass)


Gameplay:
I harass a lot with my TS. It's so easy to kill someone's minionwave. They are always hiding behind minions, but with TS you can get em down from a distance, making it easier to kill opponents. Furthermore I use the passive from ES to harass with. Just hit minions untill it's loaded > hit enemy champ > ES and go in for the kill if that's possible.
Once you hit lvl 6 you can really pwn your enemies if you didn't already.
The best combo for a HUGE damage boost and certain kill 1 vs 1 on lvl 6 would be:
LR > flash in your enemy for MS due to ur LR that is activated > ES for the 2nd mark > ulti = instant 3rd mark, so stun > ignite > TS (is easy hit now, cuz he's stunned) > ulti will add 2nd mark > auto atk untill ulti does last mark = again stun, or until you stun him with passive from ES. This puts out a LOT of damage and therefore you have a certain kill unless someone has around 1200+ health, which I doubt at lvl 6.

Generally this is always my combo, because you are certain to have 2 stuns. If you don't kill someone by then, you either lack damage or you are focusing a tank.. Either way is bad ;)
Also in teamfights this combo is killing.
LR > flash > ulti > ES > ignite tank (because he has to die in the end ^^) > pick off squishy newbs with your TS > chase people that didn't get stun already (while your ulti is still on ofc..).

Work in progress..
Please be kind and have some time :)

Work in progress..

Yet to be discovered more about.

With these runes and Doran's shield you will start with 712 Health, which makes you pretty strong earlygame.

(More to come xD)