There are many ways to listen to and download audio from videos on YouTube. Some even give the possibility to directly record the mp3 file on your smartphone.
You will have the choice between free solutions but not necessarily 100% legal or solutions paying if you do not want to take the risk of breaking the law.
The simplest way, but also the most expensive, is to subscribe to the subscription 'YouTube Premium' or 'YouTube Music'. These services provide you with additional features that allow you to download music and videos to YouTube through a dedicated application. You will have access to all your recorded music when you are no longer connected to the internet.
You also have alternatives to these paid solutions. These will allow you to download your mp3 for free, but are a little more complicated to use. In fact, you have to go through a youtube converter.
Online you will find sites like MP3hub.com, Onlinevideoconverter.com or flvto.biz that give the ability to convert a video to MP3 from its YouTube URL. You can then download it to your smartphone or computer.
In addition to the websites listed above, you have a multitude of other websites offering a YouTube video converter. The best way to find one is to do a Google search using the keywords below:
Generally, you need to copy the address or URL of the YouTube video and put it in the expected location in the Youtube video converter. Then, you choose the format of the file to download and you save. Once downloaded, you'll just have to add the file to your music library.
Some MP3 video converters do not allow you to directly download music to the smartphone. If this is the case with your converter, first save the file to your computer, and then transfer it to your handheld.