Magic
[...] much of the terminology surrounding magic - "mana", "aura", even the word "magic" itself - imply a sort of ephemeral, mysterious force of nature that can neither be tamed nor understood. Indeed, it must have seemed as such to our forebears who coined these terms. But in today's enlightened times, these confusing implications only serve to intimidate and discourage our would-be scholars. The principles of magic are no less concrete or consistent than gravity or friction [...]
Magic refers to the use of mana - a mysterious substance that appeared in the world after the Cataclysm - to warp reality. Mana can change into other forms of energy, temporarily condense into a matter-like state, create time/space anomalies, and so on.
Humans, spirits, and monsters can all use magic in different forms, and it can also be automated by building spells into magitech machines.
Spirit Magic
Monsters and spirits can control the mana that makes up their bodies to use magic, as easily as a human might control their arm. Most monsters only have one or two abilities that seem to be determined at creation, while spirits are intelligent enough to use magic to its full effect. Thus, this form of magic is usually referred to as spirit magic.
Theoretically, spirits have fine enough control over mana that they can do anything with their magic. They have been known to heal wounds, conjure visions of distant places, attack from a distance, etc. with ease. However, they are limited by their mana reserves, both in type and amount. For example, a fire spirit like Salamander can't conjure water and would have a difficult time levitating an object, since he lacks the water and air elements. Furthermore, a spirit who uses too much mana at a time is at risk of dipping below their condensation threshold, at which point they will dissolve back into loose mana and die. Large-scale reality alterations such as time travel or permanently transmuting matter would require so much mana that they are beyond any spirit's capability.
Spellcasting
Being made of physical matter and not mana, humans cannot directly use magic. However, they do have a unique ability to absorb mana from their surroundings, store it in their bodies, and manipulate it. When mana is manipulated into specific shapes (called spells), it activates and produces a particular effect based on the spell's geometry.
Theoretically speaking, the right spell can replicate any magical effect a spirit can produce, but in practice humans are heavily limited by the finicky and specific nature of spellcasting. For example, there is no general-purpose levitation spell; for every object you want to levitate, you will have to adjust the spell to account for its location relative to you, how much force you want to exert, and so forth. This means complex magic like healing and divination are practically impossible without a spirit's help. On the other hand, since they draw mana from the atmosphere and not their own bodies, human spellcasters can cast spells with any mana type requirement and aren't in danger of dying from magic overuse.
Each spell consists of a circle and some number of glyphs. The circle encloses the glyphs and tells the mana to interpret everything inside it as a single spell, while the glyphs specify the spell's effect. Most known glyphs are directly pulled from the ancient writings of the Telos civilization from 1000 years ago. New glyphs can only be found through trial and error - drawing random shapes and observing the effects - which is both time-consuming and dangerous, as some glyphs have immediate and violent effects. It's unknown if the Telosians had a better method for discovering glyphs; if so, it's been lost to time.
While many people can use a few spells as part of their everyday jobs, only certified scholars who are capable of inventing their own spells can be called mages.
Magitech
Read more: magitech
The Telos civilization had machines capable of casting spells, but the theory behind why they worked was lost, leaving humans unable to recreate them. This changed about two centuries ago with the rediscovery of magesilver, a metal that attracts, stores, and conducts mana in a similar way to human bodies. If magesilver is shaped into a spell and a mana current is run through it, the spell will be cast in the same way as if a human mage shaped that spell. Using this basic principle, humans have created kitchen appliances, high-speed trains, and even rudimentary portal-phones to make their lives easier.
Magitech machines can store a lot more mana than a human and spells too complicated for a single mage to draw on the fly, so they have a reputation of being powerful and reliable. However, they can't change their own circuits to account for different situations, so they're also inflexible; despite the leaps and bounds made in magitech in recent years, human mages won't be out of a job anytime soon.