Magic Resistance (or MR) is a stat that all units have, including minions, monsters, and buildings. Increasing magic resistance reduces the magic damage the unit takes. Each champion begins with some magic resistance which may increase with level. You can gain additional magic resistance from abilities, items, and runes. Magic resistance stacks additively.
Damage reduction
 Note: One can include the magic penetration in all the following ideas by enumerating it with a due amount of corresponding negative MR.
Magic resistance reduces the damage of incoming magic damage by a percentage. This percentage is determined by the formula: Damage Reduction = total magic resistance ÷ (100 + total magic resistance). For example, a champion with 150 points of magic resistance would receive 60% reduced damage from magic damage. Incoming magic damage is multiplied by a factor based on the unit's magic resistance (same with armor):
$ \pagecolor{Black}\color{White}{\rm Damage\ multiplier}=\begin{cases} {100 \over 100+{\it MR}}, & {\rm if\ }{\it MR} \geq 0\\ 2  {100 \over 100  {\it MR}}, & {\rm otherwise} \end{cases} $
Examples:
 25 magic resistance → × 0.8 magic damage (20% reduction).
 100 magic resistance → × 0.5 magic damage (50% reduction).
 −25 magic resistance → × 1.2 magic damage (20% increase).
Stacking magic resistance
Every point of magic resistance requires a unit to take 1% more of its maximum health in magic damage to be killed. This is called "effective health".
 Example: A unit with 60 magic resistance has 160% of its maximum health in its effective health, so if the unit has 1000 maximum health, it will take 1600 magic damage to kill it.
What this means: by definition, magic resistance does not have diminishing returns, because each point increases the unit's effective health against magic damage by 1% of its current actual health value whether the unit has 10 magic resistance or 1000 magic resistance.
For a more detailed explanation, see this video.
 Unlike health, increasing magic resistance makes healing and shielding more effective because it requires more raw damage from your enemies to remove the bonus health granted. This is called indirect scaling.
Magic resistance as scaling
These use the champion's magic resistance to increase the magnitude of the ability. It could involve total or bonus magic resistance. By building magic resistance items, you can receive more benefit and power from these abilities.
Champions
 and
 and
Runes
Neutral buffs
Increasing magic resistance
Items
Champion abilities
Runes
Neutral buffs
Ways to reduce magic resistance
List of champions' magic resistance
Most ranged champions, shapeshifting champions who can become ranged in one of their forms ( , , , ), have base magic resistance of 30 − 38.5 (based on level).
, andThere are a few exceptions:
 37 − 58.25 (based on level) with
 30 − 47 (based on level) with
 34 − 42.5 (based on level) with
 33.5 − 101.5 (based on level) with
 26 − 34.5 (based on level) with
 28 − 49.25 (based on level) with
 32 − 57.5 (based on level) with
 34 − 42.5 (based on level) with
 32 − 61.75 (based on level) with
 39 − 60.25 (based on level) with
 30 − 51.25 (based on level) with
 25 − 30.1 (based on level) with
Optimal efficiency (theoretical)
 Note: Effective burst health, commonly referred to just as 'effective health', describes the amount of raw burst damage a champion can receive before dying in such a short time span that he remains unaffected by any form of health restoration*. Unless champion's resists aren't reduced below zero, it will always be more than or equal to a champion's displayed health in their health bar and can be increased by buying items with extra health, armor and magic resistance. In this section, effective health will refer to the amount of raw 'magical damage' a champion can take.
In almost all circumstances, champions will have more maximum health than magic resistance, thus a single point of magic resistance will give more 'effective health' to a champion than a single point of health. However, if there is a case where max health is below the value of 'magic resistance + 100', the opposite becomes true.
Because of this relationship, theoretically, maximum effective health is attained by ensure that you have exactly 100 more max health than magic resistance, regardless of how much health or magic resistance you actually already have.
 Example: Given a theoretical situation where you start off with 1 health and 1 magic resistance and are given an arbitrary sufficient number of stat points (x ≥ 100), each of which you can use to increase either your health or magic resistance by 1 point, the way to maximize your effective health is to add points to your health until your health has 100 more points than magic resistance, then split the remaining stat points in half and share them between your health and magic resistance.
However, this is only theoretically true if we consider both health and magic resistance to be equally obtainable resources with simplified mechanism of skill point investment. In reality a player buys these stats for gold instead. So when attempting to ensure the balance of 'health = magic resistance + 100', consider it through gold value distributed to the stats. Because the gold value of 1 health is roughly 7 times smaller than 1 point of magic resistance (as of V8.7), distribution per point of health or magic resistance should be 12.5% gold into health and 87.5% gold into magic resistance once the 'health = magic resistance + 100' equilibrium is reached.
This model is highly simplified and cannot be exactly applied when buying any other item that aren't purely magic resistance or health oriented as they deviate the equilibrium. Going even further, the continuous model simplifies a discrete character of real shopping, as you cannot really buy 1.125 × 450, so you either opt to buy a single or a single , drastically unbalancing the equilibrium.
forBroadly speaking, items which provide both health and magic resistance give a very high amount of effective health against magic damage compared to items which only provide health or only provide magic resistance. These items should be purchased when a player is seeking efficient ways to reduce the magic damage they take by a large amount. Furthermore, these items are among all available items the best ones to distribute their gold value equally among both health and magic resistance, thus working perfectly for rule of preserving equilibrium.
Conclusion
This information is strongly theoretical. Due to how there are many variables aside from health, magic resistance and gold value, "true equilibrium" is too complicated and unrealistic to achieve. However, a player can develop their intuition to itemize towards this equilibrium in a timely manner through the experience gained from the multitude of plays they perform.
The important thing to remember is that there is no reason to hold to the equilibrium too strictly, or else you might just lose the fun out of the game.
Trivia
 The old stat icon for magic resistance was a blue recolor of the old stat icon for armor, which seems to based on the old icon of .
Last updated: March 12, 2018, patch V8.5
 One of the biggest amount of magic resistance any champion other than a with , can obtain is 1752.994415 (which reduces magic damage by 94.603%), being a level 18 .
 Base stats: 39.85 MR
 Runes:
 Items:
 1
 1 near 3 enemy champions
 1 fully stacked
 A combination of 3 of the following:
 Buffs:

 Items = + + + = 420 MR
 Runes =
 MR = 420 + 128 = 548 bonus MR
 bonus = 27.5 + 548 × 0.16 = 115.18 bonus MR
+ = 128 MR
bonus MR:

 Base stats: 39.85 MR
 Items = + + + = 420 MR
 Runes = + = 128 MR
 Buffs = + = 145.18 MR
 MR Amplification = 1 +
 MR = (39.85 + 420 + 128 + 145.18) × 2.2105 + = 1752.994415 MR
+ = 2.2105
MR:
 Prior to Patch 3.10, a level 18 with 1 , 5 , 3 points in Resistance, 3 points in Legendary Armor, , , , , an allied aura, a full page of Scaling Magic Resist runes, and active gave a total of approximately 1004 magic resistance. Switching for and having an enemy with the same setup use on and the allied use on the enemy , yielded a total of approximately 1297 magic resistance. This is the highest possible amount of magic resistance, which is 92.8% reduction.
 If disconnected from the fountain and had the same setup, he will have 2108 magic resistance. This is a 95.5% reduction.
 NOTE: This calculation does not include the Defender mastery.
Offensive  Ability power · Attack damage · Attack speed · Critical strike chance · Critical strike damage · Armor penetration · Magic penetration · Life steal · Spell vamp · True damage 

Defensive  Heal and shield power · Health · Health regeneration · Armor · Magic resistance · Tenacity · Slow resist 
Utility  Cooldown reduction · Energy · Energy regeneration · Mana · Mana regeneration 
Other  Experience · Gold generation · Movement speed · Range 