How to transfer iTunes library and interface organization to Music on a new iMac?

I want to transfer the iTunes library and interface from my old iMac into my new iMac, but I can’t see how to do this. The Music program in the new iMac is supposed to replace ITunes, and I’ve managed to transfer the iTunes library, but not the interface, i.e. the neat organisation of composers and playlists. Music seems to provide no way of organising the library in this way. It looks as if Music is intended simply to get Mac-users to purchase music from the Apple store. All of the music in my iTunes library came from downloaded CDs,but I see no way to download CD through Music. Has anyone else had this problem?

[Re-Titled by Moderator]