Narcissism  nar·cis·sism/ˈnärsəˌsizəm/

Excessive or erotic interest in oneself and one’s physical appearance.

Extreme selfishness, with a grandiose view of one’s own talents and a craving for admiration.

narcissist (plural narcissists)

Person full of egoism and pride.  A person who is overly self-involved, and often vain and selfish.

One who shows extreme love and admiration for oneself.

Psychoanalysis . a person who suffers from narcissism, deriving erotic gratification
from admiration of his or her own physical or mental attributes.

Narcissism is a term derived from Greek mythology. Narcissus was a handsome youth who fell in love with the nymph Echo, but when she spurned his advances, he was doomed to fall in love with his own reflection in a pool. He pined away his whole life obsessing about his image and eventually turned into a flower, the narcissus.

The myth of Narcissus has given rise to the personality disorder known as narcissism, which is characterized by vanity, conceit, egotism, and self-obsession.

The simple term for narcissism is selfishness.