Prompted by
@LibraryJoe here are some quick thoughts about Manu Maugain's "Méthode d'accordéon" books 1-3, primarily from the perspective of a fairly experienced (intermediate/advanced) long-term piano accordionist newly learning the CBA. Also some thoughts on how the single Galliano PA/CBA tuition book compares to the 3 Maugain volumes. All the Maugain books teach core accordion skills, but as someone trying the switch the basic things about music theory and the left hand side are less useful, whereas the right hand development is more new and helpful. And just for clarity's sakes the Maugain books are all focused on the CBA completely, and not intended for PA learners.
Maugain Book 1 ("Débutants"): This assumes no prior knowledge of music theory or the accordion, and teaches basic music theory, different note lengths, bellows use and left hand side chord techniques. For the right hand side it starts with a very limited range of notes, with good repeated exercises, before moving to cover the whole lower C to middle C octave, then the octave below, and the octave above. Fingering guides are given especially earlier on. There are extremely good repeated exercises to develop right hand skills, including moving about up and down the octaves. Throughout the volume a series of increasing in difficulty tunes are given, allowing the growing techniques to be practiced. ISBN 9790230968584.
Maugain Book 2 ("Perfectionnement"): This continues the learning, again covering essential left and right hand skills, as well as more music theory. It is full of a set of increasingly difficult tunes, with more rapid note changes. As well as tunes later with e.g. fast triplet runs it has a section teaching playing two notes at a time on the right hand side, and later three notes together are covered. For the piano to CBA switcher this book is best worked through fairly quickly from start to end, and will probably not pose major challenges, with the key additions to the right side technique more limited here. There are also fewer core exercises that you would want to repeat, though the tunes that build up the techniques are full of content that will develop key skills. ISBN 9790230969970.
Maugain Book 3 ("Virtuosité"): This looks to take things to another level, with seriously advanced content! For the right hand side there are again excellent and increasingly ambitious exercises, alongside tunes to practice these on. In terms of playing multiple notes at a time the book takes you to up to five notes simultaneously on the right hand side, with initially at least CBA fingering helpfully indicated. It also develops musicality and extremely fast note transitions, with lots more great exercises and also tunes to practice this. By the end you should be able to play just about anything on the CBA. ISBN 9790230973885 (note this volume includes a CD).
By comparison Lucien and Richard Galliano have a "Complete Accordion Method" for both PA and CBA single volume book (ISBN 9781540034953 in English, also available in French). So in page count that's about 1/3 of the total length of the Maugain books (the Maugain books are each about 100 pages, and ditto the Galliano in English language version). Leaving aside the question of which course suits which type of player best - and that really is an individual decision to make - looking through the book I'd say that most of the Galliano book gets only a little way into the equivalent of volume 2 of Maugain. But then in the very last few pages of Galliano there are extremely concentrated exercises playing up to 4-note chord harmonies on the RH. But these lack the many pages of training exercises and tunes to develop these skills that Maugain book 3 has. So ultimately if you want to play tunes like that, get the Maugain 3.
At the moment I'm newly working through Maugain 2, but have already picked up multi-note harmony and fast triplet skills myself from my own arrangements that I want to play. So I expect to work fairly steadily through Maugain book 2 alongside learning other tunes myself. All going well I will continue onto Maugain 3. But that will be a much harder challenge. Maugain 1 took me about 6 months to get through, slowly, but I still regularly play its core exercises and some tunes.
I think for an experienced PA player going to CBA Maugain 1 is a great book to develop basic competence. Maugain 2 doesn't have as much new RH content, but has some excellent exercises and incrementally difficult tunes that are worth playing. But it's not as big a step up for the new learner as book 1 is. And book 3 is just on another level.
As for which is best I'd suggest getting both Maugain 1 and Galliano, and trying them out and seeing which works for you. I did this early on, and ended up sticking with the Maugain. It just suits me better. But you can also mix and match.