Soul

The soul (魂) is an aspect believed to be the spiritual essence of a living being.

Principles
The soul is said to be an incorporeal part of a living being, holding their spiritual essence and consciousness.

In many cultures, after a person's death, their soul is believed to persist, leaving the body and passing into an afterlife realm, often dictated by their actions in life (such as with Heaven and Hell), or move through the cycle of reincarnation to be reborn in a new body and start life anew. In some stories, there are souls that are barred from the afterlife and left to wander the earth, or linger as ghosts due to the nature of their death or unfinished business. There are often various rites intended to assist the soul in its passage, and figures believed to act as guides. There are also some means intended to communicate with the souls of the dead.

There are also various stories of people who sold their own soul to a supernatural entity, such as the devil, in order to achieve a goal or attain power.

The Imagine Breaker apparently doesn't work on souls, even if they are of supernatural origin.

Magic
Despite the fact that modern magic revolves around refining life force into magic power, few magicians have a clear answer as to what the soul actually is. There are various theories, some more prominent than others, but there is little proof as to which is correct.

Though the mechanisms of the soul are not fully understood, there are magical methods to duplicate it and magicians can create physical bodies to act as containers for the soul despite not properly understanding it. The creation of magical life forms is one example of this. There are also spells intended to affect a target's soul, and means of tracing people through magical power based on the link to the soul.

There are a number of fields of magic involving the souls of the dead, their passage and communication with them. One of these is necromancy, which includes rituals to communicate with the dead and to help them pass through the gates of heaven. In some of these rituals, necromancers can place a false soul (偽りの魄) into a corpse, in order to put the "residual memory" to rest and close its "spiritual circuit". These false souls can possess and operate corpses, being able to animate them to a certain extent and act autonomously.

Magic Names are supposedly carved onto a magician's soul.

Science
The soul is just as little or even less understood on the science side. In the past, there were a number of scientific theories made involving the soul, such as resulting in a loss of mass from a corpse after death, which have been disproven.

In modern times, on the Science Side, the soul is often seen as an occult concept and something of superstition. Despite this, there has been at least one experiment in Academy City which had observing the creation of a soul (魂の生成) as a secret secondary objective. The subject of the experiment, Kuriba Ryouko, had her body split in two and the two halves having the other half replaced with machines, forming two cyborgs. After living separately for a year, the two were recombined into one. The split apparently had the effect of creating another soul from Ryouko's, one which came to reside in the mechanical components which were left over after Ryouko's human body was recombined, and assembled.

According to Ryouko, unlike other souls, thought to be linked to the body and destroyed when it ceases to function, the doppelganger's soul is apparently merely stored inside the mechanical body and if the container was destroyed, it would be freed from its restraints and spread to its surroundings. She also theorized that the abnormal "free soul" (自由な魂) would be able to possess anything or possibly, in the worst case scenario, engulf the city itself.

Following research into where esper abilities originate from through dissection, Hishigata came to the conclusion that it had something to do with the soul.