The Science of Magic
The planet Kodu is a world of magic. There are wizards, witches, magical creatures, and even magical methods of travel. So how does this happen on Kodu but not on Earth? Well, to be honest, before the Starfall that destroyed every city on Kodu, the elves were far more advanced scientifically than humans ever were. Because of millennia of scientific research, the elves became more capable at magic than humans ever were.
At the very deepest level, magic is the manipulation of two sub-atomic particles known as Allokos, and Tháumos. Allokos is the particle of order, structure and potential. Tháumos is the particle of change, energy, and possibility. These particles have quantum mechanical barriers and therefore, in nature, cannot interact with each other. However, if those quantum mechanical barriers can be overcome and the allokos and tháumos particles are allowed to interact, magic occurs. Someone who has Romi, which is the strength to bind the allokos with the thaumos in the right combinations, can cause a quantum event known as a Tarachi which is a disturbance in the fabric of reality, which the commoner calls magic. Manipulated properly a tarachi can heal wounds, turn a sword into a plowshare, and cause a dog to speak any language you desire. It all depends on the discipline used and how it's applied.
Sometimes a commoner will assume that wizards and witches accumulate allokos and thaumos, but on Kodu they are always available to a wizard or witch. Allokos and thaumos are common parts of the fabric of life. Another misconception is that of mana. Commoners believe that wizards accumulate mana, and they cannot do magic if they do not have enough mana. Mana does not exist; there is no such thing. The commoner may be confused about a wizards romi, his strength to manipulate allokos and tháumos, but in reality the main reason why a wizard won't do magic is because he doesn't want to or doesn't see a need to do it. Occasionally it is because he doesn't have the strength or the imagination (fantasia) to do the kind of magic requested. And lastly (and most often) it's because you didn't pay him enough. (Even wizards need to eat)
Magical Disciplines
Magevo or Witches Magic
Common tarachis spun by an adept at magevo is often used for healing wounds. They often use magevo to help crops grow, or pickled vegetables to ferment faster, sourdough starter to rise faster, or dye fabric without dyes. Witches can leave their body behind and accompany an animal, fly with a hawk, run with a stag. This is called Enosi or Joining. It's not a permanent thing, when the animal is tired of enosi, the animal kicks them out. Successful levitation and locomotion while levitating is the sign of a skilled witch. Witches do not need a broom to fly, but straddling a broom prevents people on the ground from looking up their skirts. They don't need a familiar, but cats and owls are fun to have around and don't mind trainees attempts at joining. Witches Magic is often called "kitchen magic."
Duke Nicholas Stein is an advanced adept at Magevo, but he says it gives him a headache to use magic.
Magos or Wizard's Magic
While a witch can learn her craft in a few years, Magos or Wizard's Magic takes decades to learn. It combines advanced manipulation with quantum entanglements, but it also requires intense study of the world around. Alignment of the stars often makes binding the allokos with the tháumos much easier and a wizard is able to do so much more during a Stardance. The results of magos is only limited by the wizard's fantasia (imagination), his romi (strength), and the amount of training he has had.
Note: while a wizard may be able to change shape to a lion, they are a man dressed like a lion, they don't know how a lion thinks or communicates. Duke Nicholas Stein was affected by ancient Elven magic, Vanemate Rasside Jõud, the Power of the Elder Races. This made Duke Nicholas a Polyeidus, a person who can actually become those creatures. When he becomes a different creature, he can think and act like that creature. According to Elven legend, only an elf is capable of becoming a polyeidus.
Gois or Enchanter
Gois is the most powerful adept at Magos. What makes a gois is not the amount of study, but romi, their natural strength to manipulate allokos and tháumos. They are so powerful that they can perform tarachi inside their targets mind. If they can achieve that, without destroying their target's mind, they don't need to become a lion, their target or targets will see them as a lion. Enchanters are rare. Neth Skelm was an Enchanter.
Goissa or Enchantress
A goissa is a female enchanter, also known as an enchantress. The enchantress is considered dangerous because she can manipulate a man's sexual desires and enslave him, but that is a two edge sword. If an enchantress manipulates a man (or woman) to desire her, she in turn ends up feeling the same desire toward her target. It is rumored that Duchess Octavia Stein is an Enchantress which would make her the most powerful magic user on Kodu. It is also said that she had enchanted Duke Nicholas and often wears a gown that is completely transparent to the man she enchants and to tease him, she wears it at palace functions. Rumors abound that she uses the enchanted staff Virga with the ancient artifact the Orb of Jørn as a long-range weapon.
Magical Species
Fairies
Fairies are the most magical of all humanoid species. Everything about them is magic, without magic they would not exist. They can understand and speak any spoken language, and read any written language. They can lull any baby to sleep with their singing and are adept at telepathy but it bothers most humans. Contrary to common belief, fairies reproduce sexually, in fact sometimes that's all they do. Humans have a hard time telling male fairies from female fairies, but they don't need to know. Only the fairies do.
Elves
Elves are the most magically powerful species of humanoid on Kodu. It is said that an elf wizard is born skilled in manipulating allokos and tháumos and their training is mostly a matter of teaching themselves to control their impulses. There are few elf wizards and elf witches. The wizards serve elven royalty and rarely speak to anyone outside of the royal classes, but there are rumors of elven wizards in Teurnia, a non-elven kingdom. It is said that elves are being trained in Magevo in Uduithia, a human kingdom with elf villages.
Humans
A human that is skilled enough to properly manipulate allokos with thaumos is rare. Often it's found that the best wizards have some elf ancestry. Humans have built universities to train human wizards with mixed results. Vampires and Werewolves are humans that were cursed by an elf wizard in their ancestor's past. They have high romi or strength but lack the imagination to manipulate allokos and thaumos into something useful.
Gnomes
Most gnomes are born knowing Magevo, or witches magic, which makes them ideal garden gnomes. However, gnomes do not have the desire or strength to advance their magical abilities.
Dwarves
Dwarves are masters of earth and stone, great craftsmen and rune-workers. Dwarves with any magical abilities are rare but their magic is handy in shoring up new tunnels.
Goblins
Goblins are clever and cunning, they use magic in chaotic and unpredictable ways. Fortunately they are light on romi so their attacks are rare and weak. They're more effective with their claws.
Demi-giants
There is no record of a demi-giant with any magical abilities.
Ancient Elvish Glossary
Allokos = weird - a quantum level subatomic particle, the particle of order, structure and potential
Thaumos = wonder - a quantum level subatomic particle, the particle of change, energy, and possibility
Tarachi = agitation - a disturbance in the fabric of reality commonly called Magic
Romi = Strength - the ability to manipulate allokos and thaumos
Fantasia = imagination - the imagination needed to properly combine allokos and thaumos
Magevo = witch - kitchen magic (Wizards believe only females can be a witch and use magevo)
Magos = wizard - the magic of a wizard (Wizards believe only males can be a wizard and use magos)
Gois = Enchanter - Most powerful wizard (no human gois currently exists on Kodu)
Goissa = Enchantress - Most powerful female wizard (wizards claim that no female can become a wizard on Kodu)