Which specific institutions were known for storing and preserving classical works? What were their methods?
The institutions were monasteries, or to a lesser extent bishoprics, and their method was writing them down and sticking them in a corner. Or, simply acquiring a tome or scroll and sticking it in a corner. There may have been some preservation among the households of the nobility, but not to any considerable degree.
On a general scale, there wasn't much more to it than that.
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