The first temple was the one built by Solomon (1 Kings 6:1) beginning in 966 BC. The second temple was built by Zerubbabel (Ezra 5:2), beginning in 530BC. Although Herod rebuilt the temple just before Jesus was born, his temple is still called the “second temple”.
The third temple is the one to come. Some people believe this temple will be built before Jesus returns to earth although there is limited evidence for this in the Bible. There are, however, a number of Bible passages which mention a temple being built after Jesus returns to earth. For example, the prophet Isaiah wrote
It shall come to pass in the latter days
that the mountain of the house of the Lord
shall be established as the highest of the mountains,
and shall be lifted up above the hills;
and all the nations shall flow to it. (Isaiah 2:2)
Zechariah 14:16-21 also mentions the “house of the Lord” in Jerusalem being a place of worship in God’s Kingdom.