I myself am not really a Buddhist. I do find myself leaning in that direction, more and more, in a lot of ways -- but Buddhist beliefs are not a prerequisite for benefitting from this book. Whether you are a Buddhist or not, there's a lot to be gained from working through the exercises included herein. The value of this book to me, is the way it combines mindfulness with breathing.
Awareness guiding the body to calm, can lead the body to reciprocally calm the mind, in an ongoing cycle. If you wish to make this cycle part of your daily existence, this book can really help.
If you come to value this book, and are looking for similar techniques, ideas, etc., I would like to recommend "The Quiet Mind" by White Eagle, or "The Relaxation Response" by Dr. Herbert Benson.
This is a same "sixteen steps" for breath meditation that was practiced and prescribed by the famous Thai monk Bhikku Buddhadasa. Unfortunately, there is no way to make enough sense from the translated descriptions of Buddhadasa and his followers, that one can actually practice from what you read.
Hanh's "Awareness of Breathing" is a perfect description, and he anticipates and addresses the questions that you would definitely have from a literal reading of the Sutra. If someone wanted to practice Buddhist meditation without having a teacher, this method and this book would be my exact recommendation.