History of the Second Temple - Wikipedia
The accession of Cyrus the Great of Persia in 538 BCE made the re-establishment of the city of Jerusalem and the rebuilding of the Temple possible. According to the Bible, when the Jewish exiles returned to Jerusalem following a decree from Cyrus the Great (Ezra 1:1-4, 2 Chron 36:22-23), construction started at the original site of Solomon's Temple, which had remained a devastated heap during the approximately 70 years of captivity (Dan. 9:1-2). After a relatively brief halt due to opposition from peoples who had filled the vacuum during the Jewish captivity (Ezra 4), work resumed c. 521 BCE under the Persian King Darius (Ezra 5) and was completed during the sixth year of his reign (c. 518/517 BCE), with the temple dedication taking place the following year.
Flavius Josephus records that Herod the Great completely rebuilt the Temple, even going so far as to replace the foundation stones and to smooth off the surface of the Temple Mount. This Temple became known as Herod's Temple.
The Romans destroyed Jerusalem and its Temple in 70 CE under Titus, decisively ending the Great Jewish Revolt that had begun four years earlier. The lower levels of the Western Wall form part of the few surviving remains of Herod's complex.
Traditional rabbinic sources state that the Second Temple stood for 420 years and based on the 2nd-century work Seder Olam Rabbah, place construction in 350 BCE (3408 AM), 166 years later than secular estimates, and destruction in 70 CE (3829 AM).