Welcome to Android Central! To download music from Google Play Music, go to the Album view, tap the 3 vertical dot menu button associated with the album in question, and tap the pin icon next to "Keep on Device" so that it's upright. "Pinning" the music onto your device means it will download and be accessible by Google Play Music even if you're offline. However, this doesn't mean that you can move or copy the music around freely--the music that is downloaded goes to an obscure (and I think hidden) directory, with a coded filename. (I look at this as a soft way of discouraging music piracy.)
If you want to download your music and be able to transfer it around easily, the best thing to do is go to Google Music on your desktop and download from there. You can download each of your tracks a total of 2 times. If you use the Google Music Manager, you can download your music an unlimited number of times, but the catch is that you have to download your entire library all at once. See more information here: http://forums.androidcentral.com/ge...ide-getting-started-android-2014-part-ii.html
Thanks for yur detailed answerd, until now I used to transfer music via USB from my notebook, considering this is easier, but the methods you displayed are more comfortable