Do I have to download each individual song to be able to play it offline? I have downloaded playlist (both mine no Apple playlist) but that doesn't seem to download the songs for pay offline.

Hello mewen,
I know that it can take some time depending on how big your library is, but the answer is a yes and no. Depending on how your Apple Music Library is setup, you can actually download an album or playlist to avoid selecting each song and tapping Make Available Offline. Obviously, if random songs are in your library and not part of a Playlist or album, you will need to do those individually. Take a look at the article below for more details.
Add music from the Apple Music catalog to your library
https://support.apple.com/en-us/HT204839
Have a good day

ditto. And that's why I have today cancelled the auto subscription on the last day of my three month trial. this playlist glitch is literally the opposite of common sense. I like the playlist suggestions. I could never be bothered to make my own in iTunes. So naturally when I have a suggested playlist from Apple Music that sounds good, great, I tick it. I then realised that you also have to download for offline listening. Fine, just like deeZer. Oops. Actually, not like deezer at all. Apple Music lies to you and shows 20 tracks downloading on wifi at home. Lovely. Then half an hour later you're in the car wanting to listen to your great new playlist...and it either hangs up because you've got no 3G or 4g, or chews up your monthly data allowance. Despite specifically telling it to download the lot via wifi. This is a massive design flaw. I don't give a **** about beats radio really. If I want radio I'll switch it on. I don't care about ' connect' - id rather just go to a gig when my favourite bands play nearby. I do like playlist suggestions and all I ask is that I can download it at home on wifi with one touch and rely on it to be there when I hit the road or the gym. Clearly that's too complicated and Apple would rather I individually pressed on the submenu for every single track and downloaded it individually. my solution? Cancel Apple Music and go back to deeZer. Anything I want I can buy through iTunes for less than an Apple Music subscription or buy the cd off amazon and rip it to my Mac.

i don't think you answered his question correctly. I have the exact same problem. From how Apple describe the service, I should be able download an Apple Music playlist, and find the songs in "my libirary" section when I have the "show offline" enabled. However, I can only see the playlist downloaded, and he songs are in that playlist(if I'm lucky), but the individual songs don't appear under any other tabs, including "songs, artists, etc), which is utterly confusing. Please address this.

That's such a lame response, I can understand it if thats a temporary method with an official fix on the way, because that's not how Apple advertises the service on its website(using the link the rep attached here on this thread). We should be able to see all the downloaded songs in "songs" even if we download an entire playlist, it's just common sense. I demand a better response.

I am having this problem too, I have followed the instructions below to make various playlists available offline. The playlists are around 20 tracks. When I press the 3 dots and choose make available offline at the top of the screen it briefly says downloading 20 songs. When I go into the playlist later, none of them have downloaded to my phone. I end up having todownload each one individually.