Google Play Music for Android lets you save your favorite music for your offline usage. But you are not able to save them according to song, playlist or by album. You might want to save that music locally on your device so that it would not make the heavy load on your data plan and you will be still able to listen to your favorite music without streaming them each time.
If you want to download music directly from Google Play music app on an Android smartphone so you can use this app and method to download music from Google play store.
How to download music using Google Play Music Android application:
Step 1: First of all open Google Play Music app on your Android smartphone
Step 2: Then Search and find your favorite songs via search bar
Step 3: When you find out your favorite song or music on the screen, open it.
Step 4 : After finding your song click on the download Icon .
Step 5 : Now your song ready to download on your smartphone, or also you can play offline all downloaded songs.
After downloading music from Google Play Music apk app, you can find your music at below location
Do let us know if this helped you. Do you have any other questions? Feel free to ask in the android forum and get answered.