Every intelligent (to a certain point) living being consists of three parts: Body, Spirit, and Soul.

The Body is self-explanatory, to a point. It is obviously the physical makeup of the being in question, but it is also the properties of said makeup, such as the physics-defying nature of dragonflight and the unnatural resilience of troll hide.

The Spirit is less obvious. It is the measure of how much vital essence a creature has. It is difficult to quantify, however. Dragons must have a massive amount, surely. They are vicious apex predators, capable of generating massive amounts of fire, complex aerial displays, and stunning speed and ferocity. However, regard also the phoenix. Not nearly as bombastic, but considering it's near-infinite lifespan, it must have an astonishing amount of Spirit.

The Soul is the most mysterious of the three. It is the repository of what makes every being distinct from its fellows, and what divides savagery from sophistication: the mind. There are those in wizarding society that claim only humans have souls, but they fail at the most basic level to explain why. They claim humans are more intelligent, but there isn't a human born who can outsmart the dullest sphinx. They claim humans are more sophisticated, but the lowliest Gringotts teller has a better grasp of contract law than the most savvy solicitor. They cry that the gift of magic sets humanity apart and above of all other beings, but the most wretched house-elf can command magic on a massive scale, and the bigots conveniently ignore that the vast majority of humanity has no magic at all.

This brings us to the elements of performing magic. Magic can be roughly divided into three elements: Will, Power, and Focus. These three elements are present in every use of magic, though in different proportions depending on what type of magic is being used. The reader may have noticed that there are three elements of magic, just as there are three elements of being. This is not coincidental. Each element of being corresponds to, and actually has an effect on, each element of magic. The Soul corresponds with the Focus, the Body with Will, and the Spirit with Power.

Charms magic (magic that affects certain changes in probability) is strongly tied to Will. When performing a charm, the magic-user wills a change in reality via the use of probability. The stronger the magic user's will, the more likely the desired outcome. Power and Focus aid the change in their own ways, and belief often helps this process, which is why wand-users are told that proper incantation pronunciation and wand movement will improve their casting. It is true, but not necessarily correct. For example, practiced wand-users can simply point their wand, focus their will, and the desired outcome will occur.

The proof of the claim that Charms magic alters probability is thus: when using insufficient will to perform a charm, wildly varied things have occurred, some of them not even close to the desired outcome. Distracted magic-users have done the following to their target object when trying to levitate it (all examples below have been witnessed by multiple beings. Citations in Appendix A):

The target object has:

Caught on fire.

Exploded.

Melted.

Began to sing.

Began to sing in a foreign language, perfectly (The magic-user in question did not speak this language).

Apparently gained life (The target object in question is currently a resident of New Zealand, though Waldo the Step-Stool is not currently available for interview).

Frozen to -272 °C.

Turned to wine.

Been replaced by a facsimile of itself, composed entirely of yarn.

Began to meow and move like a cat.

As there are infinite things that could happen at any moment (however unlikely they may be), thus there are infinite things that could go wrong with a poorly-performed Charm. Thankfully, it appears that extreme negative effects (such as the spontaneous apparition of a denizen of Hell, or the annihilation of the planet) are instinctively avoided by Magic itself.

Transfiguration magic (magic that affects only the physical makeup and shape of objects) is strongly tied to Focus. Obviously some elements of Power (roughly scaled higher the larger the transfiguration) are required, or any sufficiently focussed non-magical human would be able to Transfigure like a master. In order to Transfigure, the magic-user in question must have a clear image of the desired outcome in their mind, including the size of the object and the duration of its appearance. When they decide that the target image is sufficiently detailed, they must allow their magic to come forth and make the necessary changes. Note the emphasis on "allow." A being's magic will always attempt to work on behalf of that being. [Notable in examination of powerful magic-users of history, as conflicts with less powerful magic-users nearly always go the way of the more powerful. This is an effect of probability alteration by Magic, often with bizarrely unlikely effects.] One simply has to allow magic to do as it will, and the desired outcome will result. Attempting to want the outcome often elicits similar results as a poorly-performed charm; that is to say, nearly anything. [Therefore Will is not of much use in this branch, though one could say one is willing one's self not to Will, as ridiculous as it sounds.] It is important to note that truly permanent Transfiguration is impossible, as nothing can really grasp the concept of infinity. Only through Ritual can a change be made permanent.

The last type, and possibly most poorly understood, is Ritual magic. Ritual magic is magic that can be used to change anything, and is strongly tied to Power, though use of the Mind and Body (not Soul and Will) is very important. Ritual magic works as follows:

Through use of a sacrifice, a desired effect takes place.

Obviously, it's not quite so simple as the above rule sounds, but that is the general idea. The sacrifice in question must be important to the being performing the ritual, and the more important the sacrifice, the more Power required to sacrifice it. It is vitally important that the sacrifice in question be enough to power the ritual, or the magic-user will pay a forfeit themselves, often in either pain or death. For less potent rituals, pain itself can be used as a sacrifice; or rather, the individual's lack of pain can be used as a sacrifice. For example:

A magic-user in 1685 wished to turn his leather boot-laces to silk. In order to perform the ritual, he sacrificed his dinner, allegedly a chicken sandwich. Supposedly the ritual was successful, in that his leather boot-laces were silk from then on, but his sacrifice was not deemed worthy. The outcome was not pretty. His eyes were torn out and his left thumb severed. Who or what decides whether a sacrifice is worthy is not yet known.

Ritual magic has garnered a poor reputation amongst the rank and file in the last few centuries, as powerful magic-users have used it to subjugate and destroy when they go "Dark." It is a simple thing to power a ritual when one cares more for personal aggrandization than, say, one's family or children. It has been noted that some more selfless, powerful, magic-users have sacrificed parts of their very selves that they held dear in order to exact great change upon the world.

There are, naturally, other forms of magic, such as Potions, Runes, and Arithmancy. However, these forms of magic do not actually require that those who perform them have any magic at all. Magic helps, certainly, but any non-magical human can follow a recipe, carve a line from a template, or do mathematics. The potions, wards, and foretellings garnered this way are vastly less effective, but they are effective to a certain point.