Thought I would add My two cents worth.
As a fairly new player of the concertina(I play other instruments as well)I started with and am still working through Levy's book, Since I am leaning toward the Irish sytle I have also started Bramich's "Irish Concertina". As I am new to the instrument I have found Levy's book(with Cd's) highly efective, in teaching me to use the instrument and understanding the why and the how of playing. That foundation I am building has helped with the Bramich book. If I had not started Levy's book first I think I would have just been pressing buttons.