Herodium is 3 miles southeast of Bethlehem and 8 miles south of Jerusalem. Its summit is 2,460 feet above sea level.
Herod built or rebuilt eleven fortresses. This one he constructed on the site of his victory over Antigonus in 40 BC.
Herod's Herodium

Constructed over a small pre-existing hill, the Herodium was a fortress for Herod to quickly flee to from Jerusalem and a luxurious palace for his enjoyment. He chose to be buried here and the mountain is the shape of a tumulus. Herod's tomb was discovered by archaeologist Ehud Netzer in 2007. For details and photos, see these posts at the BiblePlaces Blog.
The Palace

King Herod built the mountain by first erecting a double-walled cylinder with an outer diameter of 200 feet. There were seven stories in the cylinder including two or three at the top which no longer exist. Afterwards a massive fill of earth and gravel was placed against the cylinder. The four towers are located at the points of the compass.
The Synagogue

Probably a triclineum (dining room arranged with three tables) in Herod's day, this room was transformed into a synagogue by the Jewish rebels who took over the Herodium in AD 70.
First century AD parallels to this synagogue exist at Masada and Gamla, two sites also captured and held by Jewish fighters in the war against Rome.