There is very little written about Professor Buteyko. I have a copy of a "novelization" of his life, apparently a three-volume work for which I have the first volume. It's insightful to read but, at the end of the day, those of us who teach this really do go over all the same points.
If you understand the Bohr effect, you understand the mechanism behind what the Professor advocated. The rest is, much like we do at StrongFirst, polishing the chrome: trying to find the methods that are the most useable, user-friendly, repeatable, and give the best results.
Unfortunately, the Professor didn't teach the same thing to all of his students because, as it became clear that his work was quite controversial, he elected only to teach the least controversial parts at times. If you poke around on the Internet, you will find widely diverging views and methods as a result. Practicing "Buteyko Light" is better than nothing, but the full protocol has reversed chronic disease symptoms for many, many things, not just breathing disorders. E.g., I've never had an issue with being overweight but my appetite changed dramatically with breathing training, and I lost five pounds of bodyfat I'd carried around for years without even trying to do so. I am currently teaching someone with a diagnosis of fibromyalgia - the breathing practice doesn't cure the disease, whatever its cause may be, but it definitely "reverts" the symptoms - my student reports feeling better and is about to ask her doctor about trying to take less medicine for her condition.
-S-