How many temples were built in Jerusalem and when?
After a few sackings by hostile forces the Temple was completely destroyed around 586 BC by the Babylonians.
The second temple was the Temple of Zerubbabel built starting around 538 BC. This temple also came under attack and was nearly destroyed several times. This caused it to be repaired and rededicated, latest being done by Herod the Great. Which is how it was in the time of Christ.
It was destroyed by the Romans in 70 AD.
There has been a few attempts in building a third temple. They have not been successful.