The concept seems very good for those who are new to proofs (and logic), but the way it is carried out is a bit chaotic. Specifically, although the author starts the reader off with one basic proof "rule" per section, the names given to the rules/symbols by which they are denoted in proofs are difficult to remember, especially as they begin to accumulate in subsequent sections. These rules are VERY basic, and would probably bore anyone besides slower math students. Having recently finished a book on basic logic, I found that I pretty much knew them all already. Also, though I'd had little practice writing proofs myself, having read textbook proofs here and there over the years was enough to put my ability level beyond this slow-paced book.
Throughout the book, the author introduces the reader to various subjects in abstract mathematics and provides some appropriately basic theorems that are subsequently used in the proofs. This is good if the reader desires a survey of math in one book.
I would hesitate to recommend this book to anyone, regardless of mathematical background. If looking at a math proof leaves you absolutely baffled and almost completely unable to follow the reasoning, and you want to jump into math proofs immediately at the shallow end and are willing to plod along with the author's symbolic system, then you may want to try this book. You would probably have a firmer grounding in the reasoning process if you start off learning basic propositional and predicate calculus (aka symbolic logic 101), then move on to a basic text on a relatively simple system of abstract math, such as number theory or set theory. When you come to a theorem, try to write the proof yourself, then compare your work to what the author did. Symbolic logic will give you meaningful terms for the rules of inference used in proofs and present them in a universal (not just mathematical) context, making them easier to remember. Logic 101 is also probably a good introduction for those who have stronger linguistic skills than math skills.
If you are a bit more comfortable/ambitious after logic 101, and the sort of student who learns better knowing "why" before the "what," (meaning you learn better from following pre-set rules than seeing examples) you may even want to try to find a simple text on mathematical logic.
I'm using both of these methods simultaneously, and it seems to work well.