Tapping on the thumbnail begins playing all of the songs of a genre. The trick is to tap the thumbnail for a genre instead of its name from the list of genres. Instead, you are taken to a list of the albums from your library in that genre, which lets you play a single album but not all of them. If you tap on the name of a genre from the list, you don't begin playing the whole genre. From the Library view of the My Music tab, choose Genre (or Artist) from the header below the Recently Added belt. The tricky thing about starting a genre shuffle is actually starting to play a genre. From the expanded mini-player, you can tap the shuffle button at the bottom, letting you listen to a shuffled mix of your songs rather than alphabetically by song title. Tap a song to begin playing it and then tap the mini-player to expand it. You will now have a list of songs at your fingertips. From the Library view (as opposed to Playlists), choose Songs from the header below the Recently Added belt. If you want to shuffle all the songs from your music library or, say, a genre or an artist, however, the shuffle button is dastardly hidden. When you are viewing a playlist or an album, the shuffle button is right where you would expect it - easily accessible at the top of the of the list of tracks. Like many things in Apple Music, the shuffle button is buried amongst the clutter.