In this video you will hear all Professor Layton's Themes, I added 'Records of Memories' as an extra, because you can clearly hear his theme in the song. I know his theme can also be heard in other songs, but I only chose to add 'Records of Memories' as it is only clear in this song.

Timestamps:
00:00 || Professor Layton's Theme
02:10 || Professor Layton's Theme (Live Version)
05:46 || Cold Open Professor Layton's Theme
08:23 || Extra Records of Memories
09:39 || Escape!
12:00 || The Puzzle Explained!
14:32 || Professor Layton's Theme (PLvs.PW Version)
16:03 || Professor Layton's Theme (PLvs.PW Version No.2)
17:27 || Professor Layton's Theme - Museum March