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I intersected two layers and now I would like to merge the rows that have the same id while adding up the last column using QGIS.

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Use Menu Processing / Toolbox /Aggregate and set Group by expression (NULL to group all features) to the field containing the information about the group to which should be merged and the Umfang field to sum - in general, check for each field the aggregated value you want to get:

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You get a new layer as result: a copy of your input layer, but with a reduced no. of features and aggregated values as you defined it in the dialog:

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