Apple does not allow users to remove entire albums, instead we have two options; delete a single song at a time or delete the entire library. Learn how to delete your entire library here.
Open the music player and locate the song you want to delete. Left swipe the song to delete it. This method works on locally stored songs.
Deleting Songs That Cannot be Deleted
If you are having problems removing a song, this is because it is linked to iCloud which affects purchased songs. This method is for deleting songs that you could not delete using the previous method.
1. In this example, I am deleting the song, “Ribs”, by Lorde. Swipe left at the song and hit delete.
You will notice the song is still there in the music library. At this point, swiping left at the song again will do nothing.
2. Go to Settings -> Music – > Show All Music – Make sure this option is turned on
3. Go to iTunes Stores -> Purchased and re-download the songs you wish to delete by pressing the cloud button.
4. Go back to Settings -> Music -> Show All Music – Disable this option now
5. Open the music player and locate the song. Swipe left to delete. This time it will actually get deleted.