That book uses an own method, by the author, a kind of mix of different methods that many people use. It's until now the closest to what I learn from my teacher.
Some other methods include:
Suzuki - http://www.suzuki-music.com/
This is a general educational method, just as Plato, Aristotle,
Taubman Method - http://www.balancedpianist.com/bptaubman.htm
No idea what it exactly is, but it's taught by Robert Macdonald at Juilliard and Robert Shannon at Oberlin (I heard from another forum).
There are plenty of methods, I just can't name them all because I don't know any more. You can google to find more or something.
EDIT: A guy called Kreisler at another forum posted this:
Every teacher has his or her own particular way, but at the beginning level, it mostly boils down to Suzuki, Russian/Chinese and what most people call "Traditional."
The Suzuki approach is for children and approaches the ear first. The Russian/Chinese approach focuses on the development of musicianship through technique, and "Traditional" lessons typically focus on reading. Examples of the "Traditional" approach include the ABRSM syllabus and most MTA syllabi in the United States.
Also, most "self teaching" methods focus on reading and/or chordal approaches. (There's no such thing as self-taught Suzuki, and a self-taught Russian approach wouldn't make any since because the training of technique is highly dependent on someone diagnosing your problems and showing you what to do.
EDIT 2: I see that you have also posted in that forum