I have this map
and I want to put these red circles in the legend of the map according to this form:
Is there a way to do that in QGIS?
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QGIS can not produce a legend like the right one on your color plate 1.2. There is a currently outstanding feature request to add size-scaled features to the legend in print composer, but it has not yet been implemented. Best try would be to generate it in a third party software or some drawing application, and then add the legend as an image to the print composer layout.