Manchester Central Library is not only architecturally impressive with its neoclassical style (shaped like a pantheon), it also houses a huge collection of publications on various media.
The shape of the building is circular so, when you are on one of the upper floors and you walk along, before you know it, you find yourself where you started without realising you're going round in a circle.
The building also houses the Library Theatre which regularly hosts high profile productions.
St Peter Square (tram stops there too) next to the town hall. www.manchester.gov.uk/libraries/central/index.htm
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