The Kurpfälzisches Museum — the Museum of the Electoral Palatinate — occupies a handsome Baroque palace on the Hauptstrasse and is the principal history and art museum of Heidelberg. The collections cover the city and the surrounding Palatinate region from prehistory through the medieval period and up to the 19th century, with particular strength in the history of the Electoral court at its height in the 16th and 17th centuries.
The undisputed highlight is the Zwölf-Apostel-Altar (Altar of the Twelve Apostles), carved by Tilman Riemenschneider around 1509. Riemenschneider was the greatest German sculptor of the late Gothic period, and this work — twelve limewood figures of the apostles of extraordinary refinement and expressiveness — is one of his masterpieces. It was originally made for the Windsheim altarpiece and came to Heidelberg in the 19th century; it now has its own dedicated room.
Other notable holdings include a cast of the jaw of Homo heidelbergensis, one of the most important human ancestor fossils found in Europe (discovered near the city in 1907 and dated to roughly 600,000 years ago), as well as an extensive collection of Romantic-era paintings of Heidelberg and the Neckar Valley. The museum is uncrowded even in summer and provides a useful context for the castle and city if you visit early in your stay.