Damage modifier

Damage modifiers refer to the buffs or debuffs to a unit that causes it to deal or receive increased or decreased damage. These are percentage values. They don't add extra flat damage but modify all damage normally done. These buffs or debuffs are only received by champion abilities, neutral buffs, on-hit effects from items and masteries.

Damage dealt modifier
These are buffs that allow the champion that has them to deal increased or decreased magic or physical damage from autoattacks, abilities, item's actives and. The raw value from the attack or ability is increased or decreased by the modifier and then applied to the target.

All damage dealt modifiers stack multiplicatively. Since multiplication is, the order is irrelevant. So if uses an autoattack on a CC'd champion just after using a maxed  on it, while affected by, his autoattack's damage will be modified by 107.525% (110%115%85%).

Champion abilities
Note: Only the damage modifier effect of these abilities is shown here, to read more information on each of these abilities, follow the link on each of them.
 * grants his basic attacks additional 10% true damage.
 * allows her to recast a spell with increased damage.
 * grants 50% additional damage to targets below 15% health.
 * allows her to focus intensely on one single target for seconds to deal  increasing her damage to it from all sources.
 * deals 2.66% increased damage for each 1% health the targets are missing (maximizing at ~200% increased damage when targets are at 25% health or less).
 * deal 50% increased damage against targets affected by and.
 * allows him to deal 20% increased damage when striking a unit from behind with his autoattacks or abilities.
 * grants her 100% additional damage.
 * afflicts his target, dealing damage to them over time and causing Swain to deal increased damage to it for 4 seconds from all damage sources.
 * deals 15% increase damage against champions when at maximum rank.
 * allows him to blink to his target and deal increased damage to it for the next 3 seconds.
 * allows his autoattacks to deal 10% increased damage if his target is slowed, stunned, immobilized or suppressed.
 * grants her next attack increased damage.
 * deals 1% increased damage for each 1% health the target is missing.
 * grants him 5% increased basic attack damage for each ghoul currently summoned.
 * grants him next attack bonus damage.

Masteries

 * increases your champion's physical and magical damage by.
 * increases all damage dealt by your champion by 5% to enemies under 50% of their max health.

Champion abilities
Note: Only the damage modifier effect of these abilities is shown here, to read more information on each of these abilities, follow the link on each of them.
 * enhances her, to debuff her target to deal 20% less damage for 4 seconds.
 * makes his autoattacks and reduce all damage that his target deals by 15% for 2.5 seconds.

Summoner Spell

 * reduces damage dealt by 30% for 2.5 seconds.

Damage received modifier
These are buffs or debuffs that allow the champion that have them to receive increased or decreased magic or physical damage from autoattacks, abilities, item's actives and. The final value from the attack or ability is increased or decreased by the modifier and then directly applied to the target's health.

Armor and magic resistance damage reduction percentage count as one source of damage received modifier against physical and magical damage respectively. For example, a champion with 300 armor has 75% damage reduction from physical damage.

Damage reduction from armor and magic resistance and from any other sources stack multiplicatively.

Increasing damage received
Note: Only the damage modifier effect of these abilities is shown here, to read more information on each of these abilities, follow the link on each of them.

This stacks additively and effectibly stacks additively with the effects that increase damage dealt by a unit to a unit aflicted by this debuffs.

Champion abilities

 * affects all targets hit to receive 12% increased damage from all sources for the next 5 seconds.

Items

 * causes the target to recieve a debuff which amplifies all magic damage that champion takes by 20% for 4 seconds.

Champion abilities
Note: Only the damage modifier effect of these abilities is shown here, to read more information on each of these abilities, follow the link on each of them.
 * grants him damage reduction for 7 seconds.
 * grants him 50% damage reduction while channeling for up to 2 seconds.
 * places a defensive shield on himself, decreasing all damage taken by a 30% for seconds.
 * channels for 1 second and then receives reduced damage for 20 seconds.
 * reduces all magic damage taken by 15%.
 * to grant her 15% damage reduction for 1.5 seconds after blinking.
 * takes 40% reduced damage while in stealth.
 * creates a great vortex of natural energy on a nearby area reducing non-tower damage done to allied champions in the area by 20% until toggled off.
 * reduces all damage that exceeds 10% of her current health by 50%.
 * reduces all physical damage by 50% from taunted enemies.
 * grants him 5% damage reduction for each ghoul currently summoned.

Items

 * grants the wearer 10% damage reduction from physical autoattacks.
 * grants the wearer 10% reduced magic damage.

Masteries

 * reduces all damage taken by 3%.
 * reduces damage taken from critical strikes by 10%.
 * reduces damage taken from turrets by 5%.

Damage immunity
There are some instances in the game where a champion is immune to receiving any kind of damage (including true damage) for a few seconds.

Champions

 * grants the target ally champion damage immunity for seconds.
 * grants her damage immunity from all sources except from her target for seconds.

Items

 * grants the user damage immunity for 2 seconds.

Flat Damage Reduction
Several champions have abilities that reduce damage by a flat amount. Flat damage reduction is factored in after armor or magic resistance(verify? Sion's page disagrees). This makes it significantly better the more resistances you have. In addition, periodic damage effects will have each tick of damage reduced. For example, ticks 8 times, so 1 flat damage reduction would reduce its total damage by 8.

Flat damage reduction does not work against true damage.

Champions

 * provides physical flat damage reduction.
 * provides flat damage reduction against auto-attacks.
 * provides a 40% chance to ignore flat damage against auto-attacks.

Items

 * blocks 8 damage from champion basic attacks.

Masteries

 * reduces damage taken from champions' auto-attacks by 3.
 * reduces damage taken from monsters by.
 * reduces damage taken from champions by.