They believe that it is where Muhammad ascended to Heaven.
Jerusalem (Al-Quds in Arabic) was and still is important to Islam because in Islam it is the place where Mohammed ascended to heaven.
The prophet Mohammad died and his spirit ascended into heaven. He was not translated i.e not tasting death. But before this Muhammad was pulled by winged horses and flown over Jerusalem and ascended to heaven accompanied by the angel Gabriel. The rock which he ascended from is now a monument inside "The Dome of the Rock" .
The Dome of the Rock Shrine in Jerusalem marks the spot where Muslims believe that Mohammed ascended to heaven before returning to Earth.
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The holy city of Jerusalem, the place where Christ was crucified, was buried and came back to life and then ascended into heaven.
It is thought that Mary grew up in Nazareth and, possibly, Jerusalem. After Christ ascended into heaven she spent time in Ephesus and Jerusalem.
There is no extra-biblical evidence that Jesus ascended to heaven.
Act 1:12 Then they returned to Jerusalem from the hill called the Mount of Olives, a Sabbath day's walk from the city.
The prophet Elijah ascended into the heavens.
The rock from which the prophet Mohammed ascended to Heaven.