I ripped everything here from the Mistborn fandom page if you want to read it there
https://mistborn.fandom.com/wiki/Allomancy
https://mistborn.fandom.com/wiki/Feruchemy
Allomancy is one of the three magic systems in the Mistborn fantasy novel trilogy, as well as the most prominent. People capable of Allomancy are known as "Allomancers" and have the ability to use or "burn" metals to fuel a variety of physical and mental enhancements or abilities. For an additional burst of power, Allomancers can burn their metal quicker (or "flare"), consuming it faster but also gaining far greater benefits in return.
A person who can only burn one metal is known as a Misting while those born with the ability to burn more Allomantic metals are known as a "Mistborn". There are sixteen metals Allomancers can use: 8 basic metals (4 base, 4 alloys) and 8 higher metals (4 base, 4 alloys); there are also 2 additional metals referred to as God Metals that sit outside the main 16, which have as many as 16 alloys each, including Malatium. All these metals must be pure when ingested while the alloys need to be mixed in specific proportions; if the metals are impure or the alloys are mixed incorrectly, the Allomancer could become ill or even die.
The Allomantic metals come in four groupings of four metals: Physical, Mental, Temporal, and Enhancement. Each of these 4 groupings has 2 base metals and their corresponding alloys, which in turn have a related ability. Each metal produces an "Internal" or an "External"; a "Push" or a "Pull" effect.
Individuals who flare their metals intensely for extended periods of time may be physiologically altered by the constant influx of Allomantic power. These Allomancers are known as Allomantic Savants. These people experience heightened ability, and heightened dependence upon, whatever metal they are burning in such a manner. Without powerful external intervention, it is believed that this process is irreversible.
Basic Metals
The metals and alloys below are the 8 basic Allomantic metals. The metals here form two groups: external and internal. External metals allow a Misting or Mistborn to exert control over their environment. Internal metals allow a Misting or Mistborn to exert better control over their body.
Physical
Steel
Coinshots have the ability to burn Steel, which allows them to "Push" on nearby metals. This can allow them to make metallic objects that weigh less than they do to fly through the air away from them (using coins, for instance, as weapons). For metallic objects which weigh more than they do, this can cause them to be pushed away from the object. It was generally assumed that a Coinshot could not Push on metals that pierce or are otherwise contained in the body of another Allomancer (e.g., ingested metals), however it can be achieved by an exceedingly powerful Allomancer or Hemalurgist.
Aluminum and several of its alloys cannot be "Pushed" or felt by a Coinshots; thus a Coinshot can be killed by an aluminum bullet.
Iron
Lurchers have the ability to burn Iron, which allows them to Pull on nearby metals. This can allow them to make metallic objects that weigh less than they do to fly through the air toward them. For metallic objects which weigh more than they do, this can cause them to be pulled toward the object. It was generally assumed that a Lurcher could not Pull on metals that pierce or are otherwise contained in the body of another Allomancer (e.g., ingested metals), however it can be achieved by an exceedingly powerful Allomancer, or a Hemalurgist.
Aluminum and several of its alloys cannot be "Pulled" or felt by a Lurcher.
Tin
Tineyes have the ability to burn Tin, which allows them to enhance all five of their senses. Tineyes are often used as lookouts and scouts because they can see in near-darkness. A major flaw of burning is that if a sudden loud noise or bright light appears it can render a Tineye stunned for a short time. Tin also gives mental "stability" allowing the person to utilize all of the information that it provides and allowing them to assess a battle situation quicker than a normal person. The increase given compares in no way to the mental increase given by atium.
Pewter
Pewterarms, or Thugs, have the ability to burn Pewter, which allows them to greatly enhance their physical capabilities. While burning pewter, a Thug can fight or perform physical labor longer than any normal person, and is also many times stronger than his or her normal self. This enhanced strength also allows a Thug to shrug off wounds that would kill or incapacitate a normal person. Pewter-burning also provides a Thug with an increased sense of balance and vastly increased speed and dexterity. A Thug performing a "pewter drag" can run for many hours at speeds up to approximately that of a galloping horse. This is extremely draining on the Allomancer's body and will require the Allomancer to burn pewter after completing the pewter drag itself, just to keep the person's body from collapsing in near-death exhaustion.
One danger for a Thug is when the Thug carrying something that they normally could not carry and they run out of pewter to burn, the object they are carrying will crush him or her, causing serious injury. Another danger is that a Thug who shrugged off earlier wounds could succumb to said wounds when they run out of pewter to burn.
Mental
Bronze
Seekers have the ability to burn Bronze, which allows them to determine if someone is using Allomancy in the immediate area. With practice, an Allomancer can determine the location of the other Allomancer, which metal the other Allomancer is burning, and to what extent the other Allomancer is burning his or her metal. An extremely powerful Allomancer can penetrate the copperclouds of other weaker Allomancers, but only if they (the more powerful Allomancer) are given a Hemalurgic spike for Bronze and had natural Bronze Allomancy.
Copper
Copperclouds[1], or Smokers, have the ability to burn Copper, which allows them to hide themselves and others from "Seekers" by dampening Allomantic vibrations caused by burning metals. The area hidden by a Smoker is known as a coppercloud (hence the name).
In strike teams, Smokers are extremely helpful to keep from being caught by a Seeker, or a Mistborn burning Bronze.
Exceedingly powerful Mistborn or Seekers can pierce copperclouds and feel the dampened allomantic vibrations. The only known cases are Vin[1] and the Steel Inquisitors, because they were usually Seekers and had a Bronze Hemalurgic spike.
Zinc
Rioters have the ability to burn Zinc, which allows them to inflame the emotions of those nearby. This can be used to incite riots (hence the name) or to enhance any emotion of the target. A Rioter can affect a single person or all the individuals in a particular area.
In Alloy of Law, it has been revealed that when one's head is being protected by aluminum or its alloy, they cannot be affected by the riot effect of zinc.
Brass
Soothers have the ability to burn Brass, which allows them to soothe or guide emotions in a particular direction. A Soother can affect a single person or all the individuals in a particular area.
In Alloy of Law, it has been revealed that when one's head is being protected by aluminum or its alloy, they cannot be affected by the sooth effect of brass.
Higher Metals
The below metals are known as the higher Allomatic metals. Previously thought to be exclusive to Mistborn, it has been revealed that Mistings of the higher metals are possible.
Temporal MetalsGold
Allows an Allomancer to see what they might have been if they had made different choices in the past. It is rarely used due to possible severe emotional trauma and its questionable usefulness.
A misting who can burn gold is called an "Augur."
Electrum
An alloy of gold, allows an Allomancer to see into their own future, which effectively disables Atium.
A misting who can burn electrum is called an "Oracle."
Cadmium
An Allomancer burning Cadmium can subtly pull on time in a bubble around them, stretching it and making time pass more slowly. A Misting who can only burn Cadmium is known as a "Pulser". Once a time bubble is set by a Pulser, it cannot be relocated once the metal is continuously being burnt. Any human located within the bubble when it is set could feel the effect, and can see a "blur" of movement outside the bubble as time is seemed to be compressed. No one can either enter or leave the bubble until the metal is extinguished, while any object (e.g. bullet) tries to pass through the "boundary" would find the moving path unpredictable. When both Slider and Pulser burn their metal at the same time and set their bubble at the same location, their effects cancel with each other and nothing happens.
This metal made an appearance in The Alloy of Law.
Bendalloy
An Allomancer burning Bendalloy can subtly push on time in a bubble around them, compressing it and making it pass more quickly. A Misting who can only burn Bendalloy is known as a "Slider". Apart from that Bendalloy can compress time instead of stretching it, it obeys laws as Cadmium, e.g. not being able to be relocated, any object passing through the "boundaries" would have an unpredictable moving path, etc. People outside the bubble can see a "blur" of movement inside if they watch carefully as time is being compressed. When both Slider and Pulser burn their metal at the same time and set their bubble at the same location, their effects cancel with each other and nothing happens.
Enhancement
Aluminum
Drains all other metal reserves of a Mistborn, leaving them powerless. This metal was known to the Lord Ruler and his Inquisitors, evidenced by the fact that Vin was forced to swallow it during her imprisonment in Kredik Shaw in book one. The Inquisitors kept the metal secret, however, because of its potentially powerful application.
A Misting that can burn Aluminum is known as an Aluminum Gnat, due to the uselessness of this ability on its own.
Duralumin
An alloy of Aluminum and Copper, Duralumin reacts with other metals currently burning to create an exceptionally large flare of the metal, consuming the remaining supply.
A Misting that can burn Duralumin is known as a Duralumin Gnat, due to the uselessness of this ability on its own.
Chromium
Chromium destroys another Allomancer's metals, just like Aluminum does to one's self. A misting who can burn chromium is known as a leecher. There must be physical contact.
This metal made an appearance in The Bands of Mourning.
Nicrosil
An Allomancer burning Nicrosil causes the target Allomancer's currently burning metals to be burned in a brief, intense flash. Similar to Duralumin, differing only because Duralumin is an internal metal (target is the Allomancer burning it), and Nicrosil is an external metal (target is other Allomancers). There must be physical contact.
A misting who can burn Nicrosil is called a nicroburst (Nicro)
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Feruchemy is the second magic system in the series. Feruchemy works differently from the other magics. While an Allomancer burns metal to gain power, a Feruchemist must provide the power for the magic from their own body, storing it over time for use later. Feruchemist use the same metals as storage units; commonly referred to as "metalminds", to store up and expend their stored power.
The major strength of Feruchemy is the speed at which one can access its power. An Allomancer has limits to how much power they can draw at once; while a Feruchemist can draw out the power of the metalmind with virtually no upper limit, exhausting it in one massive burst if they so choose. For instance, a Feruchemist tapping a pewtermind can be far, far stronger than even a very powerful Mistborn burning pewter, if only for a short time.
Metals
Iron: Stores Weight. Less weight slows descent . A Skimmer Ferring using this will decrease the pull of gravity on them in exchange for increasing it later.
Steel: Stores Physical Speed. A Steelrunner Ferring using this will be physically slower now in exchange for being faster later.
Tin: Stores Senses. A Windwhisperer Ferring using this will become less sensitive in one of the five senses of his choice (sight, hearing, touch, smell, taste) in exchange for heightening that sense later.
Pewter: Stores Strength. A Brute Ferring using this will lessen their strength so they can increase it later
Zinc: Stores Mental Speed. A Sparker Ferring using this will think very slowly in exchange for thinking faster later.
Brass: Stores Warmth. Firesoul Ferrings using this will cool themselves in exchange for being able to warm themselves later by tapping the metalmind.
Copper: Stores Memories. An Archivist Ferring using this will be able to store memories inside copper, forget it, then will be able to recall it with perfect clarity later while withdrawing it from the metal.
Bronze: Stores Wakefulness. A Sentry Ferring using this will sleep or be drowsier now in exchange for staying awake longer later.
Cadmium: Stores Breath. A Gasper Ferring may hyperventilate while storing breath in exchange for eliminating or reducing the need to breathe later on.
Bendalloy: Stores Energy. A Subsumer Ferring using this can consume large quantities of food and store the calories in the metalmind, in exchange for reducing or eliminating the need to eat later on.
Gold: Stores Health. A Bloodmaker Ferring using this will feel sick now in exchange for increased regeneration and healing later.
Electrum: Stores Determination. A Pinnacle Ferring using this will become depressed in exchange for a manic state when tapping the metalmind.
Chromium: Stores Fortune. A Spinner Ferring will become unlucky during active storage in exchange for increased fortune later.
Nicrosil: Stores Investiture. Little is known about Soulbearer Ferrings.
Aluminum: Stores Identity. Trueself Ferrings can store their spiritual sense of self within an aluminum metalmind.
Duralumin: Stores Connection. A Connector Ferring can store spiritual connection inside a metalmind, reducing friendship and outside awareness during active storage, in exchange for the ability to quickly form friendships and relationships while tapping.
Atium: Stores Age. A Feruchemist using this will become older now in exchange for become younger later, the same amount of years for the same time.
Allomantic and Feruchemic Combinations
If an Allomancer Mistborn also can use Feruchemy, then certain synergy combinations can result. This is most evident in the Lord Ruler, who possessed every Feruchemical and Allomantic power. A person who possesses one Feruchemical ability and one Allomantic ability is called Twinborn.
By burning a metal containing a stored attribute, such as burning atium which contains youth, the user effectively makes a profit on the attribute stored in the metal due to allomancy's property of drawing power from the metal. Thus the user gains more of the attribute than invested. A Twinborn who can do this is called a Compounder. An example of this process is the Lord Ruler's immortality which he achieves through periods spent aged and sickly, storing youth in atium and health in gold, which he later burns and stores in the main metalminds which sustain him. With effectively limitless amounts of youth and healing, he convincingly posed as a god. Note that the attribute stored must have originated from the user, hence Vin's inability to use the power in Sazed's pewtermind.
If a Feruchemist taps an ironmind and steelpushes or ironpulls, then they can increase their weight to become the anchor for the push or pull, even if an enemy also manipulating the piece of metal weighs more, or the metal weighs more than the user. One could also decrease their weight to gain more movement of their own body from each push or pull.
If a Feruchemist taps a Pewtermind, Steelmind, Bronzemind, and Goldmind and Allomantically burns Pewter, they will gain increase in Strength, Speed, Wakefulness and Health beyond what one would normally be able to achieve. This will work if you tap smaller combinations of those minds, however, only for the attributes you tap.Likewise, if a Feruchemist taps a Tinmind and Allomantically burns Tin, then their senses will increase beyond what one would normally be able to achieve.
If one Allomantically burns a metal then fills the Metalmind of the same attribute, they can fill the metalmind without lessening that attribute. This is why one might burn pewter to fill a Goldmind, then fill an Atiummind and tap the Goldmind, possibly creating the Lord Ruler's ability to live forever. This is most prevalent with burning pewter, which can fill Pewtermind, Steelmind, Zincmind, Brassmind, Bronzemind, and Goldmind.If a Pewtermind is filled using Allomancy burning pewter, then the Feruchemist won't experience an increase in muscle size when they tap their collected strength from the Metalmind. This allowed the Lord Ruler to tap enormous strength without revealing his use of Feruchemy to onlookers.