The stages is what is confusing here. There was the first time the Israelites entered Israel under Joshua. Hundreds of years later, they were temporarily exiled to Assyria and Babylonia, and permitted ot return after the time of Cyrus. The poorest Jews still remained in "Israel" while the majority were exiled. After the Bar Cochba rebellion of 132-135AD, they started to drift away from Israel settling around the world as they were barred from even seeing Jerusalem. The third time they have returned is after the second world war, if that is what you are referring to.
These are not commonly referred to as stages. Nevertheless, for Christians the Jews were expected to return back at some time. Jesus said the Jews in Jerusalem wouldl not see Him again until they acknowledge Him as Lord, "as He who comes in the Name of the Lord" (Matthew 23v39). Therefore for the prophecy to be fulfilled they had to return. "All Israel will be saved" (Romans 11v26). So the Jews will remain in Jerusalem until Christ's return, before He does that many will become Christians or Messainic Jews. Of-course the present Jewish Orthodoxy do not accept this but already many have become Christian in recent years. Figures of membership of Jews for Jesus for example have steadily risen. I hope this does answer your question.
Cyrus.
KING CYRUS THE GREAT conquered the Babylonian or Chaldean Empire and gave the Babylonian Jews permission to return to their homeland of Judah and rebuild their sacred Temple.
They were exiled by Nebuchadnezzar of Babylonia.
Cyrus II (Cyrus the Great) freed the Jewish Exiles from captivity
Israel, comprising ten of the twelve Jewish tribes, was exiled 133 years before Judah was exiled.
Jews in general never left Israel willingly. They were taken out of the land by force and taken to the conquering countries home land to become slaves or worse to be tortured and killed.
Several tens of thousands of Jews returned; some under Zerubavel, and others a couple of decades later under Ezra and Nehemiah. They gained governorship of the land of Judea under the hegemony of the Persians, and rebuilt the Temple in Jerusalem. See also:More about NehemiahJerusalem's historyTimeline
The Jewish people are descendants of Abraham through his son Isaac and grandson Jacob (Jacob was given the name Israel by God, in Genesis ch.35). The name "Jews" comes from Judah, the fourth son of Jacob, since the bulk of the other tribes (other descendants of Jacob) were exiled by the Assyrians and did not return. The descendants of Judah were also exiled (by the Babylonians) but returned to build the Second Temple not long afterwards, and their descendants are extant to this day.
That depends when. The answer that you may be looking for is that they were exiled to Babylonia.See also:Reasons for the Destructions
The exile of Judah (the tribe of Yehudah) is the same thing as the Babylonian Exile, which took place for seventy years, some 2500 years ago. The Babylonians, who destroyed the First Temple, exiled the people of Judah to Babylon; and they were allowed to return to Israel (Judea) seventy years later, under Cyrus. (Actually, it involved the two tribes of Judah and Benjamin. The other ten Israelite tribes weren't involved, since they had already been exiled 133 years earlier, and ended up in more distant locations.)
The exiled aristocracy from Judah was permitted to return to try to reclain their estates. Half did, but the remainder had become entrenched in Babylon that they declined. Both communities prospered.
The Assyrians exiled the Ten Israelite Tribes, and the Babylonians exiled the tribes of Judah and Benjamin.