Dream interpetation is a part of psychoanalysis; the seminal work on the subject is The Interpetation of Dreams by Sigmund Freud.
Joseph in the Old Testament interpreted the dreams of a Pharaoh of Egypt.
Interpretation of dreams is also a part of contemporary pop or new age culture. See new age dream interpretation; Edgar Cayce on Dreams by Harmon H. Bro, 1968; and Edgar Cayce...