Psychological projection or projection bias (including Freudian Projection) is the unconscious act of denial of a person's own attributes, thoughts, and emotions, which are then ascribed to the outside world, such as to the weather, the government, a tool, or to other people. Thus, it involves imagining or projecting that others have those feelings.
Projection is considered one of the most profound and subtle of human psychological processes, and extremely difficult to work with, because by its nature it is hidden. It is the fundamental mechanism by which we keep ourselves uninformed about ourselves. Humor has great value in any attempt to work with projection, because humor presents a forgiving posture and thereby removes the threatening nature of any inquiry into the truth.
Paleo-anthropologically speaking, this faculty probably had survival value as a self-defense mechanism when homo sapiens' intellectual capacity to detect deception in others improved to the point that the only sure hope to deceive was for deceivers to be self-deceived and therefore behave as if they were being truthful.
One modern, radical view of projections is that they are prerequisites for normal social functioning. A person incapable of ascribing their own feelings to other people has great difficulties in understanding them. Unfortunately, human beings have done great harm laboring under the delusions of projection. This is especially true for historical cases of projection between ethnic or cultural groups, for example in Apartheid or Nazism.
An example of this behavior might be blaming another for self failure. The mind may avoid the discomfort of consciously admitting personal faults by keeping those feelings unconscious, and redirect their libidinal satisfaction by attaching, or "projecting," those same faults onto another.
Projection reduces anxiety by allowing the expression of the unwanted unconscious impulses or desires without letting the conscious mind recognize them.
According to Sigmund Freud, projection is a psychological defense mechanism whereby one "projects" one's own undesirable thoughts, motivations, desires, and feelings onto someone else. It is a common process that every person uses to some degree.
To understand the process, consider a person in a couple who has thoughts of infidelity. Instead of dealing with these undesirable thoughts consciously, they unconsciously project these feelings onto the other person, and begin to think that the other has thoughts of infidelity and may be having an affair. In this sense, projection is related to denial, arguably the only defense mechanism that is more primitive than projection. Projection, like all defense mechanisms, provides a function whereby a person can protect their conscious mind from a feeling that is otherwise repulsive.
Projection can also be established as a means of obtaining or justifying certain actions that would normally be found atrocious or heinous. This often means projecting false accusations, information, etc onto an individual for the sole purpose of maintaining a self created illusion.
Compartmentalization, splitting and projection are ways that the ego continues to pretend that it is completely in control at all times, when in reality human experience is one of shifting beingness, instinctual or territorial reactiveness and emotional motives, for which the "I" is not always complicit. Further, common in deep trauma, individuals can be unable to access truthful memories, intentions and experiences, even about their own nature, wherein projection is just one tool .
The philosopher Ludwig Feuerbach based his theory of religion in large part upon the idea of projection, i.e., the idea that an anthropomorphic deity is the outward projection of man's anxieties and desires.
Psychological projection is the subject of Robert Bly's book A Little Book on the Human Shadow. The "Shadow"—a term used in Jungian psychology to describe a variety of psychological projection—refers to the projected material . Marie-Louise Von Franz extended the view of projection to cover phenomena in Patterns of Creativity Mirrored in Creation Myths: "... wherever known reality stops, where we touch the unknown, there we project an archetypal image". .
Psychological projection is one of the medical explanations of bewitchment that attempts to diagnose the behavior of the afflicted children at Salem in 1692. The historian John Demos asserts that the symptoms of bewitchment experienced by the afflicted girls in Salem during the witchcraft crisis were because the girls were undergoing psychological projection.  Demos argues the girls had convulsive fits caused by repressed aggression and were able to project this aggression without blame because of the speculation of witchcraft and bewitchment.
When addressing psychological trauma the defense mechanism is sometimes counter-projection, including an obsession to continue and remain in a recurring trauma-causing situation and the compulsive obsession with the perceived perpetrator of the trauma or its projection.
Jung writes that "All projections provoke counter-projection when the object is unconscious of the quality projected upon it by the subject."
The concept was anticipated by Friedrich Nietzsche:
"He who fights with monsters should look to it that he himself does not become a monster. And when you gaze long into an abyss the abyss also gazes into you." 
In psychopathology, projection is an especially commonly used defense mechanism in people with certain personality disorders: