v1-4: See 2 Chr 36.22-23. Jerusalem had been destroyed because of the disobedience of the Jewish kings. It would now be restored by a heathen king. Cyrus reversed the policies of the Babylonian and Assyrian kings who preceded him.
v1: The proclamation of Cyrus was God's initiative. He had made promises through Isaiah and Jeremiah; He stirred up the spirit of Cyrus in the first year of his reign.
Is 45.1-7 actually names Cyrus, although Isaiah preceded Cyrus by over 200 years. He was the anointed servant of God, although he did not know God (Is 45.1,7). God's work through Cyrus demonstrate His own glory (Is 45.6-7).
v2: Cyrus acknowledged the hand of God upon him, and His call upon his life.
v3-4: Cyrus invited God's people, not Gentiles, to return to Jerusalem. He also made provision for those who wished to return.
Since Jerusalem was central to Jewish life and faith, it was important that the testimony in Jerusalem be restored.
v5: At the same time, God stirred up the spirits of His own people to respond to the call; see John 3.8; we cannot guess where God will work, for He is not bound by human reason.
v6: Many Gentiles helped by providing articles of gold and silver. In a similar way, the children of Israel had received wealth from the Egyptians.
v7: Cyrus also brought out articles originally taken from the temple.
v8-11: The leader of the people of Judah was Sheshbazzar, who became governor over the land of Judah. Only in chapter 2 does Zerubbabel emerge as the main leader. (Some have suggested that these two men are the same; in 6.16, we read that Sheshbazzar laid the foundation, although 3.8-10 refers to Zerubbabel.)