I would like to make a map of some trails that I walk. I would like your recommendation for Linux and Android software. The way I would like to proceed is, to hike the area with my Android phone in my pocket to record the way-points. I would then transfer the way-points into my desktop and render them into a map. I am not familiar if there is any sort of standard (possibly XML) for way-points and if there is, which Android app are available to capture these to a file. On the other side, I would like to take the way-points and translate them into a bitmap or SVG file that I can import into either Gimp or Inkscape.

Any recommendations?

I use Viking GPS Data Editor and Analyzer https://sourceforge.net/projects/viking/ on Linux for trail mapping and trail maintenance. It can combine map tiles from various sources such as OpenStreetMap http://www.openstreetmap.org/ with your routes, tracks, and waypoints. I don't know what your phone can do, but hopefully it can produce GPX files (which is the XML standard for this sort of data). Viking uses GPSBabel https://www.gpsbabel.org/ to convert to/from other formats, if you need that.

Two notes about Viking: The current version 1.6.2 defaults to a background map tile source (Mapquest Open) which was discontinued by mapquest after the release, so you have to select a different map source. Second, Viking has what I consider a bug in that it doesn't warn when quiting with unsaved data. Aside from that, I think it is a great program.