This baroque masterpiece was built by Matthäus Pöppelmann and finished in 1727. It now contains four museums: the Gemäldegalerie Alte Meister (Old Masters' Gallery), Mathematiker-Physikalischer Salon (Salon on Mathematics and Physics), Rustkammer (armory museum), and a porcelain museum.
The grounds are very well maintained in the style of typical baroque gardens, with manicured patches of grass and fountains. Over the main entrance, there is a series of bells made of Dresden porcelain that plays music on the hour.
Even if you're not into museums, it's well worth a visit.