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I need a world map, broken down to GADM 1st level. The obvious way would be to download all single country .shp files and merge them. But that is far too tedious of course.

I tried the dissolve function in QGIS on the 500mb GADM world map, but its not dissolving the entities properly. It fails in 1 out of 10 because for example there are some single points remaining which QGIS recognises as borders.

Is there any solution to the dissolve problem?

Or do you know another approach?

Or is there a 1st lvl administrative boundary .shp file out there on the internet to download?

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The normal solution is to go to Natural Earth.

You didn't say what scale you need, but the 1:10m might be useful. You can download cultural features (including Level 0 and Level 1 boundaries) as vectors.

Note that Natural Earth uses defacto boundaries, and some political entities differ in opinion (or policy).

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