Ahri, The Nine-Talied Fox the newest Champion to the league of Legends
She's a Mage Assassin with an arsenal of Skills, being heavy Ability Power based Champion she is able to Mid-Lane very well and can also perform Ganks and Teamfight CC with Charm.

Ahri's abilities allow her to be a very Nimble Champion;
Ahri's first ability Orb of Deception deals Magic Damage on the Way out, But on the Way back deals True Damage... So even if your Opponents are packing Magic Resistance your still able to Deal plenty of damage to them.
Ahri's Second ability Fox-Fire surrounds Ahri with 3 Spirit Orbs which will attack nearby enemies (Prioritizes Champions) with a reduced eff on the same target, this is useful skill to harass enemy Champions with in mid lane or as Support in a Side lane.
Ahri's Third ability Charm is an excellent combo with the two mentioned above, Charm causes the first target it hits to become Taunted meaning the Target will Walk towards Ahri for a short period of time, allowing enough time to Pop both other skills using Fox-Fire to lead and Orb of Deception to follow it up Dealing a large amount of Damage to an Enemy Champion in a short space of time.
Finally the Ulti Spirit Rush, Ahri's Ulti is a Speed Dash towards the cursor making it a useful Chase Tool and a just as good Escape Capability. When Arhi performs Spirt Rush she release's 3 essence bolts that damage 3 nearby enemies (Prioritizes Champions), Spirit Rush can be activated 3x before going on cooldown. If an enemy manages to escape from Ahri while using the Combo of Charm > Fox-Fire > Orb of Deception... You can always give chase with Spirit Rush while dealing Damage to that enemy.

In terms of Health, Magic Resistance and Armor, Ahri is a Reasonable Squishy Champion in 1 vs 1 Fights/ Teamfights, if Ahri is the Focus of the Enemy. If the combo isn't enough to deal an amount of damage suitable for a Kill then best bet its not to engage the Target again, so you can either keep harassing that target until they return to base or are killed (caught off guard or returning to base by teleport).

Pro's
-High Burst Damage
-Low CD on Abilities
-Good Escape Ability (while Ulti's up)
-Long Range CC Effect
-Very good Harass abilities


Cons
-Very low base health most of the game
-Until lvl 6 has no escape mech unless you take a utility summoner spell such as Flash or Ghost
-While Ahri can initiate with Charm she must quickly deal damage while CC'd in Teamfights

Marks:
Greater Mark of Magic Penetration
Magic Penetration is really the Only viable option for Marks, Unless you want to use Secondary runes, which I would not reccommend.
Regardless, Magic Penetration is never wasted, a good stat to have that can servery hurt an enemy Champion/Minion Wave Magic Penetration is found on little Ability Power Items, so increasing the Magic penetration will give you the edge in a fight.

Seals:
Greater Seal of Ability Power
This Seal can really be changed to a more desirable one for each person, I use Potency as early game it is quite useful in getting kills and Successfully ganking... i may even change this to HP/Armor/


Glyphs:
Greater Glyph of Ability Power
All of Ahri's abilities are Abiliy Power based, so the more AP you have the better your chances of overcoming the enemy Champion and Shorting minion waves. Use Flat AP runes because you will be getting Rabbadon's Deathcap ASAP, which will increase your AP by 30% so there is no need to have AP/per level Runes. Also increasing the Ability power in early game will enhance you abilities and improve Laning Quality.

Quintessence:
Greater Quintessence of Magic Penetration
Ahri's abilities all scale off Ability Power, so adding more penetration is a critical step towards serverly harming the enemy Champion causing them to return to their Base or leaving them on low enough life for you to get the kill in using your ulti

I build Ahri as 21/0/9 to maximize her Damage output, as well as grabbing the increased buff duration in the Utility tree.

I do not have very much to say about this because this build is quite standard AP build. It takes nearly everything that is relevant from the Offense tree. In Utility, I take Summoners Insight for improved flash, Expanded Mind as a prerequisite for Meditation.

Ahri is a Heavy hitting Mage Assassin, so the Major Items you will be concerned about are Ability Power Items and CD reduction to increase the chances of Ahri's Combo... But remember that all Playstyles are different so anyone who would like to change the Item Build is very welcome but always remember...

First of all the Items I choose and why:

Doran's Ring
With the Increase in Ability power through your Runes it is imperative as your first item,
This will Increase not only your survivabilty, but also your ability to stay in lane
+100 Health - is a good start to Surviving
+15 Ability Power - Stacking on top with your already + 15 AP from your Runes = 30 AP off the bat (Cant argue with that)
+5 Mana Regen/ per 5 sec - Its great to remain in Lane... it doesnt seem like much but it helps

Sorcerer's Shoes
Giving you Speed and Magic Penetration all in one its the best bet for Ahri

Will of the Ancients
This is an amazing Item for an AP Champion like Ahri, this gives you Spell Vamp of 25% combo it with your Passive Spell Vamp for 60% Overall

Rylai's Crystal Scepter
This is the first Item to give you the real ability to survive, while also giving you the ability to slow enemies to ensure the kill even if they flash away (Chase with your Ulti)

Morello's Evil Tome
Mainly for the Abiltiy power and CD reduction, because of Ahri's CDs being so short why not make them even shorter for added Ganking Abilty/Escape Capability

Rabadon's Deathcap
This Item is the best item to grab for an AP Champion, + 140 itself is High by any standard but it increases AP by 30%
389.22 x 30/100 = 116.76 AP
so the 30% Increase in Ability power due to this with all Items Mentioned is exactly 116.76 AP

Banshee's Veil
This is where the second Item of Survivability comes in, even with Catalyst the Protector
your survivabilty is increased by a small amount, then when Banshee's is introduced you (Should) be able to s survive a gank of at least 2 Enemy Champions if you use Ahri right


To buy a couple health potions in early/mid game to help your lane sustain.

Do not be afraid to buy wards. Remember:

Buy a Ward, Stop a Gank, Save a Life

I am probably not going to include a ward guide here, as there are millions of them out already.

Lastly, Elixirs are highly underrated until late late game. In my opinion, if you have extra money, you should buy an elixir, if you think a team fight is approaching. For example. If you know Dragon will spawn soon. Have an extra 250 gold? Buy an Elixir. You do not have to use it right away unless you need the item slot for something else. Use it just before the fight is beginning. Elixirs do not wear off after death but that does not mean that you can feed the Ememy.

Ahri's Skill Sequence's Feel Similar which ever way you decide to perform them;

Sequence 1: E > W > Q > R (Chase/Definite Kill)

Sequence 2: R (Initiate a Fight/First Damage> W > E > Q

Sequence 3: E > Q > R > W (Dealing the last Amount of Dmage needed to finish Target after Chasing)

Sequence 4 (Gank/ Teamfight): E (CC Focus Target or High AD/AP Target) > W > R (Deal Heavy Damage to 3 Champions 3x) > Q (Kills Escaping Champions/Deal True Damage for the kill)

The Sequences are pretty easy to remember, but it is just Play style and Situation that is

Ahri's Abilities/Combo's are enough to Harass/Overpower/Kill most Champions without ever getting to close to them, with that added combination of Taunting, True Damage and Chase Ability... This makes her one of the most Dangerous champions of the league.

Dont take my word for it, just look below: