Ability power

Ability Power (shortened as AP) is additional Magic Damage the champions' abilities make times their multiplier. Abilities in League of Legends that are affected by ability power have an ability power coefficient. This coefficient determines how much a particular ability will benefit from a champion's total ability power.

Calculation
The concrete Formula to calculate an ability's magic damage is: Damage = Base Damage + AP*APCoefficient. For example, if a damage spell has an ability power coefficient of .25, every 4 points of ability power will increase the damage of this ability by 1. This bonus is added before Magic Resistance. Abilities that are affected by ability power are identifiable by a bracketed plus sign with a green font, along with a number that corresponds to the applicable bonus. For example a Champion having 50 ability power who has an ability with an ability power coefficient of .7, it will display +35 ([50*.7=35]) next to the corresponding value in the UI. There is no limit for Ability Power, all bonuses gained work in an additive way.

Items
Many items exist which increase Ability Power. Some give flat amounts while others give special amounts with passives that may or may not be unique.
 * +70 AP. +57 Magic Resistance, UNIQUE Aura: Reduces the Magic Resist of nearby enemy champions by 20. 2650 Gold.
 * +20 AP. 435 Gold.
 * +45 AP. +400 Mana +25 Mana Regen per 5 sec, Passive: 3% of your Max Mana is converted to Ability Power. UNIQUE Passive: Each time your Champion uses an Ability their Maximum Mana will increase by 4 Mana, up to a maximum of 1000. This effect has a 3 second cooldown. 2855 Gold.
 * +40 AP. 860 Gold.
 * +60 AP. +10 Mana Regen per 5 Sec, UNIQUE Passive: Reduces ability cooldowns by 15%. UNIQUE Active: Deals magic damage to target champion equal to 30% of their current health (+3.5% per 100 Ability Power) with a minimum of 200 damage. 1 minute cooldown. 2610 Gold.
 * +15 AP. +100 Health, +5 Mana Regen per 5 sec. 475 Gold.
 * +30 AP. +7 Mana Regeneration per 5, UNIQUE Passive: Reduces ability cooldowns by 10%. 1245 Gold.
 * +45 AP. +35 Attack Damage, UNIQUE Passive: On attack/spellcast, increases your Attack Speed by 4% and Ability Power by 6. Lasts 5 seconds (stacks up to 8 times). 2235 Gold.
 * +25 AP. +200 Health, UNIQUE Passive: +20 Magic Penetration. 1485 Gold.
 * +75 AP. +60 Attack Damage, +20% Life Steal, +25% Spell Vamp, UNIQUE Active: Deals 300 magic damage and slows the target champion by 50% for 3 seconds (700 range). 60 second cooldown. 3625 Gold.
 * +40 AP. +20% Spell Vamp. 1200 Gold.
 * +25 AP. Passive: Gain an additional 5 Gold every 10 seconds. 765 Gold.
 * +80 AP. +350 Mana, +30 Magic Resist, +7% Movement Speed, UNIQUE Passive: 100% chance when an ability is used that your next physical attack deals an additional 100% of your Ability Power in damage. This effect has a 2 second cooldown. 3470 Gold.
 * +25 AP. 50% Attack Speed, UNIQUE: Your physical attacks shred your target doing 20 magic damage and reducing their magic resistance by 6. Magic resistance reduction stacks up to 4 times. 1825 Gold.
 * +20 AP. UNIQUE Passive: Your champion gains 8 AP per stack, receiving 2 stacks for a kill or 1 stack for an assist. This effect can stack 20 times; you lose a third of your stacks if you die. At 20 stacks, your champion's cooldowns are reduced by 15%. 1235 Gold.
 * +50 AP. +25 Tenacity. 1290g
 * +75 AP. +20% Cooldown Reduction, +12 Mana Regen per 5. 2350 Gold.
 * : +80 AP. 1600 Gold.
 * +55 AP. +50% Attack Speed, +10 Mana Regeneration per 5, UNIQUE Passive: Reduces ability cooldowns by 25% 2885 Gold.
 * +155 AP, UNIQUE Passive: Increases Ability Power by 30%. 3600 Gold.
 * +60 AP. +450 Health, +525 Mana, Passive: Your Champion gains 18 Health, 20 Mana, and 2 AP every 1 min. Bonuses cap at +180 Health, +200 Mana, and +20 Ability Power. 3035 Gold.
 * +80 AP. +500 Health, Passive: Your spell hits slow the target's movement speed by 35% for 2 seconds (15% for multi-target spells). 3105 Gold.
 * +25 AP. +250 Mana, UNIQUE Passive: 100% chance when an ability is used that your next physical attack deals 100% extra base damage. This effect has a 2 second cooldown. 1260 Gold.
 * +30 AP. +30 Damage, +30% Attack Speed, +15% Crit Chance, +12% Move Speed, +250 Health, +250 Mana, UNIQUE Passive: 25% chance on hit to slow the target by 35% for 2.5 seconds; on cast, increases your base Attack Damage by 150% for one attack. 4070 Gold.
 * +70 AP. UNIQUE Passive: Spells penetrate 40% of the defender's magic resist. 2295 Gold.
 * +50 AP. UNIQUE Aura: Gives nearby allied champions +30 AP and 25% Spell Vamp. 2100 Gold.
 * +100 AP +50 Armor UNIQUE Active: Places your champion in stasis for 2 seconds, rendering you invulnerable and untargetable but unable to take any action. 90 sec cooldown. 3300 Gold.
 * Could someone order this section from most AP to least?

Consumable

 * +20-40 AP based on champion level and 10% Cooldown Reduction for 4 minutes. 250 Gold.

Champion Abilities

 * converts 50% of his total magic resistance into ability power.
 * increases her ability power by up to 30/50/70/90/110/130 corresponding to her percentage of missing health.
 * converts 30% of her attack damage to her ability power.
 * grants him 35/50/65 ability power for 25 seconds.
 * grants nearby allied champions 6/8/10/12/14 ability power while active.
 * grants him 16/24/32/40/48 ability power while active.
 * permanently gains him 1 ability power when it kills a minion and gains him 1/2/3/4/5 ability power when he kills a champion from any damage source.
 * gives him 1 ability power per 40 bonus health.

Masteries

 * increases your champion's ability power by (0.2 / 0.4 / 0.6) per champion level.
 * increases your champion's ability power and attack speed by (1.33 / 2.66 / 4.00)%.
 * increases your champion's ability power by 10 while your spell is on cooldown.
 * upgrades your spell to increase nearby allied units' ability power by 20-70 for 20 seconds.

Runes

 * Force and Potency runes increase ability power.

Neutral Buffs

 * The buff gives 40 ability power for 4 minutes.