Jews under Persian rule
In 536 BC, Cyrus the Great, the king of the Persians conquered the Babylonian Empire. Cyrus believed that religious freedom was important to keeping his empire together, and he wanted each area (satrapy) of his empire to rule itself, so he let the Jews go home from Babylon (BA-bi-lon), ending the Babylonian Captivity. Of course the Jews were very happy. Not all the Jews chose to leave Babylon: by this time a lot of the Babylonian Jews had been born in Babylon, and people had businesses and houses and their kids were in school, so many of them decided to stay. Many of them continued to be Jewish, though, and for hundreds of years there was a big Jewish community in Babylon.
The remains of the Second Temple in Jerusalem
But other Jews, including Nehemiah (neh-huh-MY-uh), did choose to go back to Israel. When Nehemiah and his followers got back to Israel, they were upset to find that the many Jews who were still living in Israel were not following the Law strictly. Even worse, many of these Jews had married Canaanites or Ammonites or Arabians! So the Babylonian Jews worked hard to force all these other Jews to obey the Law better, because they were afraid God would be angry with them. And they rebuilt their Temple in Jerusalem (the Second Temple).
This was the time of Esther (ESS-ter), a Jewish woman from Babylon who married a Persian king and was able to save the other Babylonian Jews from being killed by Haman (HEY-man), the king's advisor. This is the basis of the Jewish holiday called Purim (POOH-rim).
At this time also was Jonah. God told Jonah (according to the Bible) to go and preach about Judaism in the Persian city of Nineveh, but Jonah didn't want to go there. Instead he got on a ship going from Joppa (in Israel) to Tarshish. After God got mad at him, Jonah did go preach in Nineveh (near Babylon). This shows that Jews travelled all around West Asia at this time.
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I learned from, and the one I give my own kids):