The first temple was sometimes referred too as David's temple. This first temple was built in the reign of Solomon, David's son. David wanted to build it. David planned for and assembled the resources to build it. However, David was not allowed to build the temple because he was a man of war. God told David via the prophet Nathan that David's son, Solomon, would build the temple. Call this temple 1.0

David's kingdom was split. Ten of twelve tribes formed the (northern) Kingdom of Israel. two of ten tribes formed the (southern) Kingdom of Judah (Judea). The temple of David was in Jerusalem which was the capitol of Judah. Temple 1.0 is still in Judea.

The northern kingdom of Israel would end of conquered by Assyria; the Assyrians carried many of the people of Israel off to other lands as captives. This was a common practice to break up people groups to make them less likely to revolt in the future. Now, only the Kingdom of Judah remained. Temple 1.0 still in Judea.

This first temple existed up through the time of Nebuchadnezzar the Chaldean/Babylonian. Nebuchadnezzar captured Jerusalem twice. The first time, the temple was left standing. Temple 1.0 still in Judea.

Judah rebelled against Nebuchadnezzar. The second time, the temple was razed. Many of the Israelites in the reduced kingdom of Judah were carried of as captives. Temple 1.0 is destroyed.

Fast forward. Nebuchadnezzar passed off the scene as ruler of Babylon. Babylon was conquered by the Medo-Persian empire during the time of Cyrus the Mede. During the time of Medo-Persian rule Israelites taken captive were allowed to return to Judah and rebuild the city of Jerusalem and repair/rebuilding was made to the temple to allow for the resumption of temple activities. Call this temple 2.0

From the standpoint of world powers, Judea was a backwater province captured by Alexander the Great, then changing ownership among the descendants of Alexander's generals. Then Rome gained influence and later control in the region. Judea was brought under Roman 'protection'. One governor of Judea was Herod the Great. Herod the Great was Governor during the time of the birth of Christ. Herod liked building things and one of his projects was to expand onto and beautify the temple in Jerusalem. Call this temple 2.1

In the late 60s of the first Century AD, There was a Jewish uprising against Roman rule and occupation. The Romans sent several legions to surround the city, lay siege to the city, capture the city and destroy much of the city. Herod's temple (2.1) was destroyed by the Romans around 70 AD. Temple 2.1 was destroyed.

There are some differences of opinion about whether Herod's temple is an upgrade or a replacement. Regardless of which view a person prefers, Herod's temple was destroyed by the Romans.

In the late 7th century, Jerusalem was under the control of Muslims. The key leader around that time was Caliph Abd al-Malik. The Caliph built the Dome of the Rock on the mount where the temple used to exist. Whether it is in the exact location of where the temple was is not clear to me (though it may be clear to someone with more precise archaeological knowledge).

Not long after that, the Al-Aqsa Mosque was added to the Temple Mount.

All that is history. My understanding of the still future events are that a temple of some sort will be rebuilt in Jerusalem prior to the return of Jesus the Christ , the Son of God (call that Temple 3.0). After the return of Jesus, a new temple will be built (call that Temple 4.0).

The Bible records that immediately preceding the last judgement, the current 'heavens and earth' will go out of existence. After the judgement, God will make a new heavens and earth. There will be no temple there because the redeemed will be in the direct presence of God; the Holy Spirit will dwell in the redeemed. No temple is needed.

Hope that helps.

Edited to fix a few typos.