Humankind cannot gain anything without first giving something in return. To obtain, something of equal value must be lost. That is alchemy's first Law of Equivalent Exchange.
Alchemy is the ancient metaphysical science/mystical art of manipulating and altering matter and, to a lesser extent, energy, by using natural energy. This act is known as Transmutation and its sequence is usually described as:
Comprehension - Understanding the inherent structure and properties of the atomic or molecular makeup of a particular material to be transmuted, including the flow and balance of potential and kinetic energy within.
Deconstruction - Using energy to break down the physical structure of the identified material into a more malleable state so as to be easily reshaped into a new form.
Reconstruction - Continuing the flow of energy so as to reform the material into a new shape.
Alchemy's use is incredibly broad and involves the reconstitution (or destruction) of any type of matter. The proper application of this craft requires not only a full understanding of chemistry, physics and ancient alchemical theory, but also a sort of natural talent towards recognizing and manipulating the physical objects with energy, which require uncommon levels of intelligence and aptitude. Those remarkable individuals capable of studying and practicing alchemy are known as Alchemists.
The potential for alchemy's usage is wide and at first glance seems unlimited, though the greatest barrier for most alchemists is knowledge (or the Comprehension stage). Alchemists can only perform transmutations on subjects they are familiar with, and the size, scale, and complexity of a transmutation is likewise linked to their individual skill and knowledge. For example, an alchemist cannot perform a transmutation on an object whose molecular makeup they do not recognize or understand. If an object made from a new alloy was presented, then it is likely that no alchemist could alter it without first being informed of the makeup of that alloy. As a result, many alchemists choose to specialize in a certain craft, such as medicinal alchemy which focuses more on biological transmutations or combat alchemy, which involves fast, practical transmutations for war. The general barrier of knowledge within alchemy is the reason that alchemists are both scholars and scientists, and often seek, preserve, and hide knowledge.
While it is not clear what inherent qualities an individual needs to be able to perform alchemy, it is known that it is connected to the Gate, as it is demonstrated that without one, alchemy is impossible.
There are many paths by which alchemists can transmute the various substances of the world, with some alchemists being said to transmute by way of the Four Classical Elements (Water, Earth, Fire, and Air) and some by way of the Three Essential Principles (salt, sulfur, and mercury), but the basic tenet at the very foundation of all alchemy is that of Equivalent Exchange.
The practice of alchemy to create objects out of raw matter or turn one object into another is widely believed to be capable of anything. Alchemy is often viewed as magical or miraculous by those unfamiliar with it, but it is a science and as such is subject to certain laws and limitations, the most important one being the concept of Equivalent Exchange "In order to obtain or create something, something of equal value must be lost or destroyed."
In standard practice, Equivalent Exchange is separated into two parts:
The Law of Conservation of Mass, which states that energy and matter can neither be created from nothing nor destroyed to the point of elemental nonexistence. In other words, to create an object with the mass of one kilogram, at least one kilogram of material is necessary; destroying an object with the mass of one kilogram would reduce it to a set of parts, the sum of which would have the mass of one kilogram.
The Law of Natural Providence, which states that an object or material made of a particular substance or element can only be transmuted into another object with the same basic makeup and properties of that initial material. As an example, an object or material made mostly of water can only be transmuted into another object with the attributes of water.
Although Equivalent Exchange governs the material transfer of matter within transmutations, each performance of alchemy requires energy to perform.
Since the alchemical forces being manipulated are not human in origin, but of the world as a whole, the consequences for attempting to bypass the Law of Equivalent Exchange in transmutation are not merely failure and cessation. When too much is attempted out of too little, what occurs is called a Rebound, in which the alchemical forces that are thrown out of balance on either side of the equation fluctuate wildly of their own accord in order to stabilize themselves - taking or giving more than what was intended is often unpredictable and catastrophic in ways such as accidental mutation, serious injury, or death.
Though no machine or equipment is needed to produce the energy necessary for transmutation, merely understanding the sequence of transmutation and the limitations of Equivalent Exchange is not enough. In order to begin an alchemical transmutation, a symbol called a Transmutation Circle is necessary. A Transmutation Circle can either be drawn on the spot when a transmutation is necessary (in chalk, pencil, ink, paint, thread, blood or even traced in dirt) or permanently etched or inscribed beforehand, but without it, transmutation is generally impossible. All Transmutation Circles are made up of two parts: The circle itself is a conduit which focuses and dictates the flow of power, tapping into the energies that already exist within the earth and matter. It represents the cyclical flow of the world's energies and phenomena and turns that power to manipulable ends.Inside the circle are specific alchemical runes. These runes vary widely based on ancient alchemical studies, texts, and experimentation, but correspond to a different form of energy, allowing the energy that is focused within the circle to be released in the way most conducive to the alchemist's desired effect.
In basic alchemy, these runes will often take the form of triangles (which, when positioned differently, can represent the elements of either water, earth, fire or air), but will often be composed of varying polygons built from different triangles. For example, the hexagram is a commonly used base rune in Transmutation Circles because it creates eight multi-directional triangles when inscribed and can, therefore, represent all four classical elements at once. Other, more esoteric runes (including astrological symbols, symbolic images and varying lines of text) are prevalent and represent a multitude of other, specific functions for the alchemical energy that is released. Like instructions in a book, the runes dictate the effect of the transmutation. Depending on an alchemist's level of skill, a simple transmutation circle can perform a wide variety of transmutations, while some transmutations are so complex that they need very intricate and detailed runes. Even an alchemist that normally does not need to draw a physical circle like Edward will occasionally opt to if the transmutation is difficult enough. In addition, the physical size of a transmutation circle is also implied to affect its power, with the effects of some transmutations increased to incredible levels when drawn to the size of cities or even countries.
While almost every alchemist needs a physical circle and the corresponding array to perform transmutation, this is technically not necessary. Alchemists who have a greater understanding of the nature of the universe and alchemy as a whole have been shown to be able to transmute simply by clapping their hands together, using the joining of their hands as a circle and "themselves" as the array. This ability appears to be limited to only those who have witnessed the Gate, and does not seem to be knowledge that can be described or taught.
Certain master alchemists have been shown to take this a step even further, able to perform transmutations without any apparent movement at all. However, whether this can be attributed to the fact that the Philosopher's Stone could bypass the need for any physical circle, or that alchemists with a greater knowledge of alchemy as a whole have no need for one is unknown.
A Transmutation Array is similar to a Transmutation Circle in that it is used to circulate the energy used in a transmutation. However, unlike a Transmutation Circle, the runes are not confined to the circumference of the circle and may use the circle only as a small aspect of their function. In some instances, a transmutation array may not even be a circle at all, using different concepts to bring about the circulation or release of the energies involved. Transmutation arrays are often found as full body tattoos on alchemists due to the shape of the human body.
Attempted resurrection is the most common method of Human Transmutation, it is not the only way to perform it. Any method of manipulation and recreation of the human body and soul is a form of Human Transmutation and will therefore call upon the Gate. This is shown when Edward uses Human Transmutation to recreate his own body, essentially using the act as an excuse to open the Gate. Despite not attempting to recreate life, doing so still enacts a toll on the user, of which a Philosopher's Stone can be used in its place.