Given that the building does not have any protective elements, such as a moat or drawbridge, it is quite possible that this is not a castle at all. Maybe this is a monastery or a country villa of the emperor. Given an extremely unusual shape, it can be also a structure for astronomical measurements.
The interiors inside the castle are very basic, though this is absolutely normal for that period of time. Inside the oldest premises of the German Wartburg castle, built in the same period, the situation is similar.
Moreover, there is evidence that the finishing work was not finished, and marble and ornamentation were looted in the 18th century.
The castle was a movie location for 2017 hit Wonder Woman, the sword “Slayer of the Gods” was kept here.
Check official website for opening hours.
Getting there: parking is bad. Near the castle, there is a restaurant parking for 10-15 cars, but it is almost always full. The nearest official parking is here N 41 04.579 E 16 16.509, 1600 meters from the castle. Theoretically, there should be a shuttle service to the castle. We parked for free here N 41 05.326 E 16 16.371 and then walked uphill, here is the start of the trail N 41 05.288 E 16 16.260.
By public transport: first by train to Andria, for example from Bari. Bus 6 runs from Andria train station to Castel del Monte from April 1 to November 1. From Andria: 8:40, 10:10, 11:40, 14:40, 15:40. From Castel del Monte: 10:45, 12:15, 15:00, 16:15, 19:00. The time can vary by 10-15 minutes.