The Temple Mount, located in the Muslim Quarter of the Old City of Jerusalem is the location that both the First and Second Jewish Temples
once stood. The Second Temple was destroyed by the Romans in 70 CE. Five hundred years later, the Chaliph Omar traveled to Jerusalem and claimed that Mohammed rose to heaven from the very same spot.
Today, the Dome of the Rock stands upon the Temple Mount. The entire area is under control of the Muslim Religious Authority and have full authority on who can visit. Everyone, except Muslims, are forbidden to take any religious items onto the Temple Mount. Therefore, if you have any sacred objects or books with you, they must be left in the security area.
In recent years, non-Muslims have been forbidden from entering the Dome of the Rock and the al-Aksa Mosque. For Jews, visiting the Temple Mount is very controversial. Some rabbis believe that since the Jewish Temple's "Holy of Holies" (ie. where the Ark of the Covenant was kept) once stood near the center of the Temple Mount, Jews are forbidden by religious tradition from entering the area. Other rabbis disagree, saying that once the Ark was removed from the Temple Mount area all restrictions were removed.
According to Jewish and Christian tradition, the Messiah can only come when the Temple is rebuilt on the Temple Mount. However, the Muslims have no intention of getting rid of the Dome of the Rock or the al-Aksa Mosque. This has created a stalemate among the different religious groups and has created a lot of paranoia and distrust. As a result, clashes at the Temple Mount erupt quite often, with creates even more religious and political strife.
For me, while the Temple Mount looks quite lovely, I think I will opt to just view it from afar. I believe that my proper place is visiting the Western Wall, not the Dome of the Rock.