Importing a CD with music between tracks

I have been trying to rip a CD, in order to be able to listen to it in my smartphone. This particular CD has music even between the tracks, i.e. there is never silence between the different tracks. When ripping in alternative ways, I either have different files, leading to a small but fully audible gap between tracks, which I find disturbing, since I know this is not the case on the CD, or I get one complete file of the whole CD (CD image in EAC and similar), which means I can’t see - on my phone’s display or in the music player on the PC - the details of the track just playing; they all have one common name.

Is there a way to solve this with Audacity? I have tried importing the different tracks into one project and aligning them so they follow each other in one row, but they still have only one name, the same I gave as name of the aup project.

MP3s have inherent silence padding due to a restriction of the MP3 format. To avoid gaps between tracks you need to use a format that does not add padding to the start or end of the tracks (for example WAV, AIFF, Flac or Ogg). Some players are able to merge MP3 files on the fly so as to avoid playing the gap between MP3 files, but that is not a standard feature for all players.

I have imported/ripped tracks from CD as .wav files all the way in order to convert them to mp3:s when I am content with the import. So I have listened to them as .wav files, and still the gap occurs. And I haven’t found a way on my smartphone to make files merge when playing.

Is that playing the WAV files on your smart phone or in some other player?

In the smartphone, and on PC, using VLC and WMP alternatively. Same result.

I’ve no idea why you should be having so much trouble (unless perhaps the CD is scratched or something). Programs like CDEX and EAC should have no problem ripping a CD accurately and VLC, foobar2000 and such like should have no problem playing the ripped WAV files, but since you are having this problem, you could try ripping the CD as one continuous track, then importing that track (in WAV format) into Audacity, then splitting it into separate tracks as described here:
Note that if you export from Audacity in MP3 or WMA format, that will create a bit of silence at the start and end of each track, so export in WAV, AIFF, FLAC or OGG format.