The Doha Islamic Art museum is a must visit. At least two hours necessary for a complete tour - make it three if you want to really appreciate all the exhibits. It provides a broad overview of Islamic art over the centuries, and provides historic insights into its interactions with European and Asian cultures. Many of the items on exhibition are exquisite and very well presented. Entry is free of charge except for the temporary exhibitions, and I was able to take photos of the place.
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