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I would like to add in the attributes of each of my roof boundaries (red polygons, which sometimes overlap) the sum of the surfaces of the (green) surfaces.

I have already tried "join attributes by locations" but some of the green surfaces are sometimes just partially on the red limits.

It leads to an error:

the area added in the attributes is the whole area of the green surface and NOT only the partial overlap

What would be the easiest approach for working with Qgis, taking into account that there are a lot of data?

red roof limits with green surfaces

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Are green areas in vector format?

Try "Vector/Geoprocessing Tools/Clip" first. This way you should get only green areas within red ones. This algorithm clips a vector layer using the polygons of an additional polygons layer. Only the parts of the features in the input layer that falls within the polygons of the clipping layer will be added to the resulting layer.

EDIT: If green areas are in raster format, you can use "GDAL/Raster extraction/Clip raster by mask layer" which can be accessed through processing toolbox.

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