Recives recommendations
Although Michael Gelb is a respected writer, that particular book on A.T. isn't so great at teaching it and reads somewhat like he wrote it for school credit, and added pictures later. Just my opinion.
I'd recommend for someone who isn't going to be learning from a teacher anytime soon that you pick up this book on the Alexander Technique principles written by Anthony Taylor in 2004. In the USA it's called "Whatever You're Doing Now You Can Do It Better!" The reason you should choose this book is that it will give you an overview of the principles about why A.T. lessons are structured the day they are, no matter what the style of teaching your particular A.T. teacher will use. It uses plain English and easy to remember metaphors and stories instead of being a collection of writing difficult to decipher. (Academics and the over educated seem attracted to A.T. So the writing on it pre-2005 or so is daunting and gives the impression that the writer is beating around the bush. The reason for that are that lessons take students bodily into really, really weird unknown and disorienting feelings while "resetting" their frame of reference about how they judge bodily location, effort and sense of weight.)
Anyway, the book is a solid foundation for learning that will help you understand it even if you can afford to take the absolute minimum of six to eight lessons or an in-depth workshop with a properly trained A.T. teacher...which is something that everyone recommends if you're serious about learning it.
It's tricky to see what is going on for the student in these video above without having an eye trained to see teeny-tiny adjustments of motion that is normally not noticeable.
You might also try the "learn it without classes from a properly trained AT teacher" strategy at:
http://performanceschool.org/?page_id=623
Also, some of the more articulate Alexander Technique teachers who have youtube videos are Eileen Troberman. The people who teach musicians "Body Mapping" are great to check out. They wrote "what every musician needs to know about the body, " (originated by Bill and Barbara Conable eons ago. There's now a very interesting animated video called "move well avoid injury on youtube also made by Barbara Conable and Amy Likover, a flautist.)
Hope that helps. Generally, learning Alexander Technique from videos and a book is sort of like learning to dance that way. So eventually getting to a "real" teacher is key - at least for the first eight lessons or so. Classes and workshops teach you the fastest, unless you really need personal help because of learning problems.