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Photo: Diego Delso, CC BY-SA 3.0 via Wikimedia Commons
Actually two museums plus a number of special exhibits, though you pay one price. English, German and Russian descriptions of each permanent collections are provided in a booklet inside each exhibit hall. Both of the main museums are quite interesting, and they provide a good idea of what Riga was like in the past.
Museum of the History of Riga and Navigation is housed by the Riga Dom Cathedral ensemble in the heart of the Old Riga, Latvia. It originated in 1773 as a private collection of Nikolaus von Himsel, a Riga doctor. It is the oldest museum in the Baltic States. Being one of the oldest museums in Europe, over the centuries it has grown into the largest collection of material evidence of the history of Riga.
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Rīgas Doms
Dating to 1207, the cathedral is one of Riga's symbols. The 6768-pipe organ inside is particularly spectacular. Besides the organ, however, the interior is rather Spartan, and may not be worth the entrance fee (even the organ is being restored, though).
A modern building with an excavated fragment of the historical fortification wall system along the river. The building has the best view terraces in Riga.
House what was gifted to Peter I and house he visited during his travels.
Individual and group fine art gallery.
Covers the dramatic events that occurred in the tumultuous final year of the USSR, when Soviet authorities sent troops into Riga to overthrow the elected Latvian government.
Statue of woman with amphora on a building.