How does Reform Judaism define who is a Jew?
Reform Judaism accepts in broad outlines the traditional definition of Jewish status: to be a "Jew" one must be a member of the Jewish people, a status obtained either through birth or conversion. Jewish identity is not determined purely by the individual. One does not become a Jew merely by declaring, "I am a Jew" or "I accept the Jewish religion." One must either be born a Jew or become a Jew through a process recognized and administered by the community.
According to halachah (traditional Jewish law), Jewish status is determined on the basis of matrilineality; that is, the child of a Jewish mother is a Jew, even when the child's father is a gentile.The offspring of a gentile mother is a gentile, even if the father is a Jew. Prior to the Rabbinic period (70 - 500 CE), we find little trace of the principal of matrilineal descent. The Bible in fact seems to recognize a purely patrilineal descent, regardless of the identity of the mother.
In 1983 the Central Conference of American Rabbis adopted the Resolution on Patrilineal Descent. According to this resolution, a child of one Jewish parent, who is raised exclusively as a Jew and whose Jewish status is "established through appropriate and timely public and formal acts of identification with the Jewish faith and people" is Jewish. These acts include entry into the covenant, acquisition of a Hebrew name, Torah study, bar/bat Mitzvah and confirmation.