What is the most simple way to convert a MP4 video to a MP3 audio file?

If you want a free video converter, you can use freemake video converter. It is free and I think it can convert your mp4 video to mp3 format audio file to listen.
You can also use Tipard Video Converter Ultimate. It is much more professional and fast, but it is shareware which means you need to pay to use the full version. It can convert mp4, wmv, avi, mkv, mov, flv, mts, m2ts, mxf, vob, ts, mod, tod, mp3, ogg, aac, wav, wma and so on.

Many free video converters can do this, freemake video converter, like handbrake, format factory and so on.
I also use iCoolsoft Total Media Converter, it can convert mp4, mkv, flv, mts, mxf, wmv, avi, mov, m2ts, mod, tod and so on. Also, it provides default mobile devices' output profiles for you, such as iphone, ipad, ipod, samsung, psp, ps3 and more.

Well, I always use 5KPlayer to convert video to MP3 files for the purpose of language learning. Add video to library , click "convert", and choose MP3.
It is free.

For free converters, handbrake is OK.
Actually VLC can convert video to mp3 too. But it is a little bit complex.

I think almost any video converter programme can do it.You can try Sothink Video Converter which is flexible and very powerful for us.

Audacity is available for all platforms, freeware and easy to use. NOTE: Read the installation instructions carefully as you may also need some support software like Soundflower. (also freeware!)

I don't want the web base solution. A converter to use off line is preferred.

If you want to convert a MP4 video to a MP3 audio file,almost any video converter can do it.However,I use dvdfab video converter most of the time.It works qutie great!