Favorite thing Islam is the state religion of Jordan but there is freedom of worship here as 10 percent of the population are christians of all denominations and a sprinkling of jews, druze and alawites. There are lots of Mosques around amman with different designs and architectural styles, mirroring the different periods of occupation of Jordan. The largest of these Mosques are the king hussein mosque (unfortunately i did not have time to visit it) and other famous mosques are Abu Darweesh Mosque, Blue Mosque, etc. The mosques have large speakers atop the minarets that calls on the faithful to prayer 5 times a day and the dawn prayers start at 4:00 am and if your hotel happen to be near a mosque, better close your window panes so you would not be awaken by the loud speakers calling the fiathful to dawn prayers.
Fondest memory amman maybe an islamic country, but it is the most westernized in the middle east and there is religious tolerance here.