Jews Return to Jerusalem Rebuild The Temple Book of Ezra and Nehemiah Describes Rebuilding (aug 1, 537 BC – dec 1, 517 BC)

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So who raised Cyrus of Persia from the north to sweep through the Ancient Near East and conquer the Babylonians? No one but Yahweh. Isaiah 41:
"I have roused Him from the north, and he has come
…And He has trampled rulers like mud,
Like a potter treading clay
…The things once predicted to Zion--
Behold, here they are!" [from vv 25-29].
Yale Old Testament pg. 261

According to the biblical text we'll be discussing soon, Cyrus in 538 gave the Judean exiles permission to return to Jerusalem and reconstruct their temple. The exiles did return; many of the exiles returned. They returned to what was now a Persian province: it's the province of Yehud; I don't think I wrote that up there. Yehud is the name now of Judea and Yehud is where we're going to get the word Jew. Yehudi is the word Jew; one who belongs to the province of Yehud. So many of the exiles returned to this now-Persian province Yehud, and they exercised a fair degree of self determination.

The books of Ezra and Nehemiah, however, contain conflicting information about the return, about the restoration, and as a result our knowledge of the timing of various events is quite poor. It's really not clear who returned first to help rebuild Jerusalem, whether it was Ezra a priest, or Nehemiah a Persian Governor
Yale Old Testament pg. 309

So that's the first very important thing that Ezra tries to do: the dissolution of marriage with foreign spouses and to establish a blanket universal ban on intermarriage, to make Israelite identity dependent on the native Israelite status of both mother and father.
His second deed is the renewal of the Mosaic Covenant. This act is reported in Nehemiah 8[:1-8]. There's an extended public reading of the Torah of Moses and that's followed then by a renewal of the Mosaic Covenant:
(pg.314)

The Book of Nehemiah opens with a description of Nehemiah's grief. He hears these reports of the terrible conditions of his people in Jerusalem sometime around the mid-fifth century and, weeping, he asks for the consent of the emperor to go to Jerusalem and to help rebuild the city. So Nehemiah travels to Jerusalem, we think about 445 BCE, and he undertakes the refortifications of the city. And he meets with opposition. There's some internal opposition. There's a female prophetess, Noadiah, in Nehemiah 6:14, who seems to be opposed to this. There's some external opposition as well from Israel's neighbors: the Samaritans, the Ammonites, some Arabs. They resent this reconstruction and they see the reconstruction of the city's defensive walls as an affront to Persian rule.
But Nehemiah continues; he gives his workmen weapons so that they can protect themselves against enemy attack and the walls around the city are completed in record time. These refortifications help to establish Jerusalem as an urban center, and eventually Nehemiah is appointed governor of Judah [Yehud], under Persian domination.
pg. 311

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