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There are numerous museums around the world with collections of ancient art. Below are several with major collections.
Acropolis Museum, Athens, Greece
Ashmolean Museum of Art and Archaeology, Oxford, UK
National Archeological Museum, Greece
Beazley Archive - Classical Art Research Centre at the Ashmolean Museum, Oxford University
British Museum, London - Includes the sculptures from the Parthenon
Foundation of the Hellenic World
Getty Villa, Malibu, CA
Hermitage Museum, St. Petersburg
Kunsthistorisches Museum, Vienna
The Louvre, Paris
Metropolitan Museum of Art, New York
Museo Archeologico Nazionale di Napoli, Naples, Italy - Major repository for artifacts from Pompeii and Herculaneum.
Museum of Cycladic Art, Athens
Museum of Fine Arts, Boston
National Museum of Asian Art, Washington, DC
Pergamonmuseum, Berlin - Contains the Pergamon Altar relocated from Turkey, as well as the Antikensammlung (Collection of Classical Antiquities) of the Staatlichen Museen zu Berlin
Pushkin Museum of Fine Arts, Moscow
Vatican Museums, Rome
Wikipedia List of Museums with Large Collections of Egyptian Antiquities