For the work I'm making, the magic system I chose is based on imagination- forcing imagination onto reality. What allows this to happen is the Mishna, a gateway between the Lower Domain and the Upper Domain. It bridges the gap between irreality and reality, using the Godhead's power to do so. It uses a lot of religious and scientific themes (it's Science Fantasy in the vein of Xenogears/Xenosaga/Xenoblade with a bit of Megami Tensei here and there).
It allows me to put giant robots, giant monsters, and sword-wielding superhumans (that can cut down both giant monsters and giant robots) in the same world.
Now, how does that affect the story? Realism. Ironic, I know, but when things feel tangible, it's not hard to convince the reader that something done isn't improbable, while also being able to make cool things happen, like making fog in winter, which isn't possible to do if you know why snow falls instead of rain.
You can find more about this in another thread where I talk further about the entire Elementalist elemental here: https://www.royalroad.com/forums/post/1110896
To make it clearer, a primitive notion could be: MOMENT (Point of time)
By combining MOMENT and a bunch of other complex terms (which are defined from primitive notions), we can get greater constructs like (some kind of) TIMELINE. It would require us to invoke a spell on primordiality (think: a source that allows creating anything) and the spell would combine whatever concepts are required to determine the properties of that timeline (eg. it could be CONTINOUS and UNIFORM). The spell in itself is nothing, but an invocation of a 'set' (for lack of a better term) of primitive notions.
This was the basis for my elemental system, I wanted something unique that relates to the idea of primitive notions. The elements like water or fire could be defined by physics, so they were bad candidates. I wanted elements to be as fundamental as they could, but at the same time, they were supposed to somehow categorize our notions and sound cool, so compromises were made.
In the end, there were eight elements (called high aspects):
Aether - responsible for existence, transformation, and creation
Nether - responsible for destruction, death, and decay
Space - related to spatial properties
Time - related to placement in time and ability to change
Order - related to frameworks (logic, math)
Chaos - related to randomness, uncontrollability, unpredictability
Psyche - related to consciousness, eg. mind and emotions
Physicality - related to physical (incorporeal included) manifestation
+ unofficial 'soul' element
What does such classification allow me to do?
I can categorize entities and spells in my world, based on the proportions of forming aspects. Eg. Rock is a Physical/Aether/Spatial/Order construct and can be influenced by an erosion spell - a combination of Nether/Time, which reduces the rock to nothing over time. It's different than standard (natural) erosion because the latter is simply an ordered (by physics) transformation of an object.
Anyway, I explore it in greater detail in 'The Red Snowman'. Chapters called 'The Academy, ...' (there're about 10).
As you can imagine, there's a lot of drama between the people who decide it's worth it to use magic and people who avoid using it all costs to keep their lifespans long and healthy. Also, form/shape magic in particular allows for some pretty surreal imagery, which is always fun to describe haha. It's probably my favorite of the subtypes to write about.
Magic is corruption from beyond sanity that seeps into the minds of mortals when they sleep and their unguarded minds are open. It can not be stopped or blocked from saturating the essence of the world, but it can be focused by a few to spare the rest. Those who can wield magic do so by siphoning the corruption seeping in and wielding it to their own souls, even if they didn't want to. That means all magic users are doomed to be consumed by nightmare and become abominations, but their sacrifice buys safe sleep and life for everyone else.
In the primary nation of the story, the ability to be "Damned" comes from the bloodlines of the three founders of the nation who slew the Abomination of "The Slaver" who controlled the population with focused corrupt power as a tyrannical living god who used human sacrifice to stave off their own demise. One who became known as "the prolific" who sired uncounted children and who's blood has passed into common parlance and who's power can rise in just about anyone who's body can bear it. The second from "the mother" who sired seven children who's children sired seven children apiece and who's bloodline is more rare but no less revered. Her power rises in those who connect to the world with a love of more than themselves, the nobility who sacrifice for the people. And the last "the legacy" who sired no children, but instead cast the last of their power out to seek and find those who had the mental fortitude to bear their curse before becoming the first of the three to be attempt Redemption, and who's tragic failure paved the way of possibility for others to succeed.
The power is revealed on a child when they come of age and manifest the mark on their left hand-- a tattoo that grows and displays their power's affinity. Overuse or underuse of the power will cause the mark to grow up their arm reaching towards their head, when the mark finally infiltrates their skull the gate to corruption is thrown wide in their mind and the Damned become Abominations-- monsters of catastrophic proportions that spew corruption unchecked into their surroundings and who's power knows no mortal limits. For that reason, all Damned are assigned a Shadow-- one part bodyguard and one part assassin, who walks with them their whole life. A Shadow's dual job is to protect the life of their charge because their sacrifice ensures the sanity and safety of the people, until they are Redeemed or Consumed-- and to kill them before their power turns a friend into fiend.
Redemption is the only other option for those who bear the burden; the full physical and mystical removal of the arm that bears the mark performed by other Damned who grow their own marks to redeem another. No Damned can or will perform a redemption until the mark passes the bend of the elbow because the Damned "owe the people that much" at least, but more commonly they wait until it gets to their shoulder before being 'disarmed'. The one armed Redeemed are revered for their service and train the new Damned with their experience and wisdom as only one who has felt the mark can really understand what it means to bear it. All new Damned are brought to the Citadel of the Redeemed, to learn what it means to bear the mark, and what it means to be the Damned saviors of humanity... and to be assigned their Shadows.
That is the magic of the Damned... nightmares made real, and corrosive magic the only bulwark keeping the sleepers sane. This is the backdrop of the whole world-- huddled masses sheltering beneath living sacrifices that keep them safe from the nightmares that hunger. Abominations and mutations that rove in the dark places of the fells that will rip that which they can not corrupt being opposed by Damned protectors. And in the other nations, other, more terrible practices are used to keep the nightmare fed... and what better blood to feed the nightmare than any other than your people's? War is near a constant threat from those who would buy a night's sanity with the blood of another, and only the Damned keep the lands secure from their corrupted neighbors. This is the story of the Nightmare plagued world, and one strange boy who was dropped at the doorway of the Citadel... the only known instance of a newborn bearing the mark of the Damned.... and his is the only mark that moves on its own.
I have other magics in place that I haven't dedicated an entire chapter to because there's not a lot to say on it.
Chaos is a corruptible magic, comparable to radiation. It's unstable and doesn't follow the same rules as the universe its placed in, which has the potential to be incredibly destructive. My main villain uses it against The Matriarch which causes permanent, magical scarring.
I have the Aether, which isn't so much as a 'type' of magic as it is the fundamental flow of life that magic actively comes from. It cannot really be affected, again, until chaos comes into play. Which my villain does.
There's other stuff too but it's more of a character driven story.
Humans and most animals are on the very bottom, so far as soul sizes go. This means that humans are technically capable of wielding magic, but casting a single spell usually results in effects similar to extreme exhaustion, dehydration, or starvation. Humans have, however, have found three workarounds to this issue.
The first is turning monsters into weapons. Residual magic remains within a monster's corpse, and that magic can be manipulated. For example, turning the bones of a dragon into a sword might get you sword that flames on command.
The second is to ask the gods for help. This is called Channeling, because you're literally channeling a god's power, a human using their own body as a medium for magic. Channeling is usually a lot slower and less noticeable than anything a god does on their own, because the human's body is a relatively fragile medium and too much magic could break it, like forcing the Niagara Falls through a kitchen faucet. Furthermore, each god has their own particular way they most enjoy being called upon. However, channeling allows for a great deal of precision, and will not leave you on death's door.
The third workaround is necromancy. Basically forcibly stealing someone else's soul/life-essence, either a human or animal, and using that to fuel your own spells, or even extend your lifespan. Humans who do that get called vampires, and are usually hunted down.
Magic overall is pretty diverse and versatile tho.