Austrian-British psychoanalyst and the central figure in the development of what is now called object relations theory. Klein moved from Vienna to Budapest to Berlin to London over the 1910s and 1920s, and her arrival in London in 1926 — at the invitation of Ernest Jones — set the stage for the long argument, the so-called Controversial Discussions of 1941–1945, between her followers and Anna Freud's more orthodox circle. The British Psychoanalytical Society eventually accommodated both by dividing itself into three groups (Kleinian, Contemporary Freudian, and Independent), and this tripartite structure has shaped British and much non-American psychoanalysis ever since.
Klein's principal innovation was the extension of psychoanalytic technique to very young children through the play technique — treating the child's play with toys as the equivalent of the adult patient's free association. What she found there, in her account, was an inner world populated from the earliest months of life by phantasies of "objects" (parts of other persons, internalized in split good/bad forms) and by primitive anxieties of persecution and loss. From this clinical material she constructed a developmental scheme very different from Freud's libidinal stages: the paranoid-schizoid position (roughly, the first months, organized around splitting and persecutory anxiety) and the depressive position (reached when the infant can recognize the good and bad object as one whole person, and can bear the guilt and concern that follow). The two "positions" are not stages to be passed through once but organizations of experience to which a person returns throughout life.
The second great Kleinian concept is projective identification — the phantasy of placing a part of the self into another person, and the corresponding effects this has on the recipient. In the hands of her followers, especially Wilfred Bion, this became a theory of how emotional states are communicated in the consulting room, and then a general theory of unconscious communication between persons. Klein's work also reshaped psychoanalytic writing on envy and gratitude (her 1957 book of that title) and on the reparative impulse behind much creative work — most famously developed in Hanna Segal's writing on aesthetics.
Klein has been criticized — by Horney among contemporaries and by many later commentators — for grounding a demanding developmental scheme in the inferred phantasies of preverbal infants. The criticism has force. Her influence on clinical practice, on object relations theory generally (Fairbairn, Winnicott, Bion), and on later work in aesthetics, groups, and organizational life has nevertheless been very large.
Klein is on the graph because object-relations theory — descended from her — supplies the picture of early psychic life that later moral and political theorists (from Winnicott to the post-Frankfurt critical tradition) have drawn on to explain aggression, group identification, and reparation. She is the pre-Oedipal floor of the graph's psychoanalytic line.