Edited for 1.0.0.108
This, as the title says, is my Mid Ap Kennen build. I am writing this guide more for semi experienced players. This being said I am not going to include what Kennen's skills do. I will use generally accepted abbreviations. If you do not understand something you should probably look it up. The only thing I will say is that when I say Shuriken I mean thundering Shuriken the ability not the shuriken used in auto attacking.

Ghost

Ghost is great for both chasing people or from running out of a gank or failed team fight. It is especially great if an enemy flashes out of you ultimate range, you can easily catch up to them.

Teleport

Teleport is great for mid because if you have to go shop or are getting harassed hard you can recall and teleport back and not lose much lane control. Late game teleport is great for returning to battle from a heal or a death. You can even teleport onto a minion in the middle of a team fight then ult and really change the tides of the team fight.

I have chosen these runes because they match my play style and have synergy with the items that I purchase.

Marks

9 x Greater Mark of Insight +.95 Magic penetration each. I chose this as my mark because it gives great magic penetration early and with the 15% you get from masteries it almost negates MR of your opponents early.

Seals

9 x Greater Seal of Vitality +1.08 health per level each. I chose this because of the health that it gives. This helps you stay alive longer and they give you a little extra health healed on level up.

Glyphs

9 x Greater Glyph of Focus +.65% cooldown reduction each. I chose this for my Glyph because I really do not feel any of the other blue glyphs are particularly worth it as much. I just feel they are the best runes.

Quintessence

3 x Greater Quintessence of Fortitude +32.4 health each. I chose this rune because of the health that it gives. I dislike buying HP items early and building my Ap items and these quints + the Hp per lvl make up for not having Doran's item.

Offense

I have 9 in offense tree for the AP per level, the cooldown reduction and mostly for the 15% Mpen. The 15% Mpen with your Mpen runes eat through most people's MR even into late game.

Defense

I have 0 points in defense. I chose to exclude points in defense because early-mid game they do not really have anything you can really depend on. Late game you should be buying defensive items and the defensive talents will not be needed.

Utility

I have 21 points in utility. I have 21 in utility because of the great versatility that the tree gives. The health regen bonus tier 1 makes up for not buying Doran's. The 5% exp boost is great for getting lane advantage with leveling faster. 3% run speed is a decent boost in speed especially if you are mid against another champion that uses skill shots or just to help you position for your own skill shots. The cooldown reduction is good because of your spell vamp you will get from items. If you can keep doing damage you can keep healing yourself keeping you in combat longer. The time dead reduction and the increase in buff duration are mainly to get deeper into the tree, but have their uses.

I am listing my skill training in the order I Max them out not in the order they appear left to right.

Thundering Shuriken

I max my Q first because the lower cooldown and increased damage. I use this for farming minions and harassing your lane opponent. Once you get into mid game and you start ganking or supporting other lanes your thundering shuriken should be max and will hit the lower level opponents for a large portion of their total health.

Lightning rush

I max my E next because it has huge damage scaling. When you max it, it should be hitting champions for about 400. This should take a huge chunk of HP out of your opponents because they should be only about level 10. Also the increase in Armor/MR is great.

Electrical Surge

I level electrical surge last because it has bad damage scaling, so I mainly use it for applying marks.

Slicing Maelstrom

I level this when i can. It is great for just about every situation. The AOE stun + and high dmg output makes it really powerful both in solo and team fights. Also do not be afraid to use it to evade a gank. If you do not have ghost up you can pop your ult and run away and they will either back off or get stunned chasing you allowing you to get away.

Starting Items

Boosts of speed and 3 health potions. The boots are great for dodging/positioning skill shots. The 3 health pots are so you can stay in lane longer. I do not always need them but I would rather buy them and not need then than to recall because i did not.

First recall

I try not to recall unless I can buy at least my hextech revolver and have lane advantage. This is only 1200 so you should get this fairly early. If you have gotten kills and have the money finish your boots, then finish your will of the ancients.

Next recall

If you continue to play like you have been(Harassing and farming) with your hextech you should not have to leave the lane until the turret is dead. You should finish your Will of the ancients and start buying Rabadon's. I try not to back until I have enough for all previous items and needlessly large rod. This means I help other lanes or just farm out. This takes about 3k gold so it might take a bit but your minion farming should be fairly solid and you can kill your lane opponent fairly consistently now.

Later Items

Ok so i recall as needed at this point. Low hp or after a push and others recall. I buy my void staff as i can. Due to the loss of Zhonya's Ring and it's synergy with Kennen's ult this is needed for survivability. I sell my will of the ancient's and buy Zhonya's Hourglass. The spell vamp late game is not as life saving as when laning because your enemies will be doing greater damage. The invulnerability shield is better. Also you will gain more AP.

Last 2 items

The last 2 items are purely defensive items. For a heavy magic team I build Banshee's Veil and Force of Nature. For a heavy physical team I build Sunfire Cape and Thormail. I chose these items because they give HP and large armor/mr + good passives. For a more balanced team I build Sunfire Cape for the passive damage and the health, then I build a Warmog's for the health and regen. Late game you need to be able to live because you will be greatly focused by the enemies in a team fight and staying alive is very important in winning team fights.

Early Game I generally just harass with Q and farm until I have an easy kill(50-30% hp left) or they have to port back. Kills are great money but if you force them to back while you can stay in lane, you will gain level advantage fast and it will be much easier to kill them down the line. Many times I find myself over extending trying to get the kill and though I got the kill, I have to recall to heal and lose the true advantage gained from the kill(Levels and damage to the turret).

Mid game I try not to recall until I can buy an item or two or if I need to heal. Kennen is not very item dependent so it is easy to hold the lane with level advantage even if your opponent has more items than you.

Late game do to your CDR and low cooldowns on your abilities you will get low on energy. In this situation I become more of a ranged caster. I just start spamming shuriken which has about a 2.5 sec cooldown and electric surge. You can still do considerable damage while still being able to stun them. This is a complete change from the normal intense fighting style he normally does so you have to be ready to adapt.