ok, I'll take a stab at this and try to tackle one of the most difficult subject, IMO, relating to Israel.
In July of 1950, Israel passed a law that basically gives every Jew the right to live in Israel. The law does not necessarily prevent non-Jews from living in Israel. On the contrary -- a very large percent of Israeli citizens are not Jewish.
Maybe a good place to start would be the law itself, verbatim.
Right of aliyah (immigration to Israel)
1. Every Jew has the right to come to this country as an oleh (immigrant).
2. (a) Aliyah shall be by oleh's visa.
(b) An oleh's visa shall be granted to every Jew who has expressed his desire to settle in Israel, unless the Minister of Immigration is satisfied that the applicant
(1) is engaged in an activity directed against the Jewish people; or
(2) is likely to endanger public health or the security of the State.
3. (a) A Jew who has come to Israel and subsequent to his arrival has expressed his desire to settle in Israel may, while still in Israel, receive an oleh's certificate.
(b) The restrictions specified in section 2(b) shall apply also to the grant of an oleh's certificate, but a person shall not be regarded as endangering public health on account of an illness contracted after his arrival in Israel.
Residents and persons born in this country
4. Every Jew who has immigrated into this country before the coming into force of this Law, and every Jew who was born in this country, whether before or after the coming into force of this Law, shall be deemed to be a person who has come to this country as an oleh under this Law.
Implementation and regulations
5. The Minister of Immigration is charged with the implementation of this Law and may make regulations as to any matter relating to such implementation and also as to the grant of oleh's visas and oleh's certificates to minors up to the age of 18 years.
Minister of Immigration
Acting President of the State
Chairman of the Knesset
Then, the law was slightly refined in 1954, basically to change a comma to an "or" and to add the exclusion of someone with a criminal past who is a "danger to public welfare", and it also changed the "Minister of immigration" to "Minister of the Interior."
In 1970, a few more provisions were added by then PM Golda Meir. Here are the changes, whic are also not very substantial, EXCEPT that it gave rise to the main issue often discusse din connection with this law, which is the definition of "Who is a Jew" to qualify for automatic citizenship rights under this law.
Here are the 1970 changes:
Addition of sections 4A
and 4B 1. In the Law of Return, 5710-1950, the following sections shall be inserted after section 4:
"Rights of members of family
4A. (a) The rights of a Jew under this Law and the rights of an oleh under the Nationality Law, 5712-1952, as well as the rights of an oleh under any other enactment, are also vested in a child and a grandchild of a Jew, the spouse of a Jew, the spouse of a child of a Jew and the spouse of a grandchild of a Jew, except for a person who has been a Jew and has voluntarily changed his religion.
(b) It shall be immaterial whether or not a Jew by whose right a right under subsection (a) is claimed is still alive and whether or not he has immigrated to Israel.
(c) The restrictions and conditions prescribed in respect of a Jew or an oleh by or under this Law or by the enactments referred to in subsection (a) shall also apply to a person who claims a right under subsection (a).
4B. For the purposes of this Law, "Jew" means a person who was born of a Jewish mother or has become converted to Judaism and who is not a member of another religion."
Amendment of section 5
2. In section 5 of the Law of Return, 5710-1950, the following shall be added at the end: "Regulations for the purposes of sections 4A and 4B require the approval of the Constitution, Legislation and Juridical Committee of the Knesset.".
Amendment of the Population Registry Law, 5725-1965
3. In the Population Registry Law, 5725-1965, the following section shall be inserted after section 3:
"Power of registration and definition
3A. (a) A person shall not be registered as a Jew by ethnic affiliation or religion if a notification under this Law or another entry in the Registry or a public document indicates that he is not a Jew, so long as the said notification, entry or document has not been controverted to the satisfaction of the Chief Registration Officer or so long as declaratory judgment of a competent court or tribunal has not otherwise determined.
(b) For the purposes of this Law and of any registration or document thereunder, "Jew" has the same meaning as in section 4B of the Law of Return, 5710-1950.
(c) This section shall not derogate from a registration effected before its coming into force.".
Acting Minister of the Interior
SHNEUR ZALMAN SHAZAR
President of the State