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I have a shapefile (one layer) with my country but I have a problem.

It is divided into 4 entries (prefectures), and I want it as one, not 4.

Also, there is a table with some data, and I want to have one row with the sum of the data. For example:

Entry  1: population 10.000, 
entry  2: population 20.000, 
entry  3: population 30.000, 
entry 4: population 40.000.

Ultimately I want something similar to this:

main piece: population 100.000. 

(I don't care if this will be done by hand, its not much work!).

I'm a new QGIS user and i don't know much. Any help would be really appreciated greatly!

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As said above and in your question the dissolve function is there. try batch dissolve and failing that try some of the solutions in Dissolve ploygons in QGIS or Grass to new polygons of defined population sizes

With dissolve you have an option to dissolve all which may need some basic tidying after the function is complete.

Hope something helps.

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