I have not been here for years, so this entry might be a bit unfair. I do remember a dry and dusty collection of archaeological relics. But this whole stretch of the Oude Turfmarkt is being done up and rebuilt by the university, so things might have changed.
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The collection includes Coptic, Greek, Etruscan, Cypriot and Egyptian relics, and special exhibitions are staged regularily. There are bits of mummies -- including several heads and feet, a jointed Greek doll from 300 BC and you can write your own name in hierogliphics. But the National Museum of Antiquities in Leiden is far superior. Leiden links
In fact, the neo-classical building housing the Allard Pierson museum was built in 1869 to house the Dutch National bank but when the bank moved out to its new home on the Frederiksplein, the University of Amsterdam bought the building. The collection, which had been on display since 1934, then moved to its present home and was opened to the public in 1976.
The collection was founded by Allard Pierson, a professor of asthetics, history of art and modern languages at the University who died in 1896. The bulk of the exhibits today come from other collections, including that of Pierson's successor Jan Six who died in 1926.