I've been working through this book independently, including all of its exercises, and I'm most of the way through. While it might not be perfect, I would definitely recommend it.
It covers many of the basics of modern logic, and serves as a good introduction for anyone, student or layman. I believe it was used for many years, and until very recently, as the set text for Oxford's first year logic course for philosophy students; so it's very reliable. One cannot really learn logic without doing exercises, so this book has a small set of exercises for every topic; if you're looking for something more discursive and readable, this might be the wrong choice. Working alone I have not found it overly difficult - in fact it's good fun - but it must be approached as a course of study rather than the way you might approach a popular science book. You won't be reading ABOUT logic - you'll be DOING logic.
There are a few things to bear in mind:
It tries to be two things at once - a layman's introduction and a textbook - and in some ways fails at both. For those studying independently there are some sticking points: just where one would hope to find much more discussion and easing in - such as the sections on formalization - you find impenetrable proofs written out in English. Minimizing the mathematics here only succeeds in confusing the reader (though maybe it was just me). And as a textbook it is also somewhat lacking, in that its small paperback format makes it difficult to work with: you'll struggle to keep it open while you've got a pencil in your other hand, and it necessitates constant flicking back and forth. I would have preferred a large format text with extensive glossary, appendices, lists of symbols and rules, all easily accessible at the back. Also, to properly learn logic you'll need more exercises than are in here.
The book uses the tableau method rather than natural deduction. I'm not experienced enough to know which is best, but in my dealings with students and philosophers it seems that the latter is favoured, especially in the context of philosophy; and it might also be worth noting that at Oxford they are moving to natural deduction for their introductory course.
The book doesn't make much of an effort to place logic in the context of philosophy, and it seems to have been written from the perspective of an overly efficient logician-mathematician rather than a philosopher. Of course, this is not an important criticism if it is used as a textbook, but if you want some background and context you'll need to supplement it with something else.
If you're looking for an introduction to critical thinking, informal logic, logical fallacies, and techniques for debate, this is not the right book. It is specifically aimed as an introduction to modern symbolic logic as it is taught academically today.
The sections on formalization can be skipped, it says, but I chose not to. I found that these sections were very hurried, and the procedures made little sense; I kept thinking "but you should explain WHY you're doing this".
Despite all this, it does achieve a balance that probably few other books achieve, between approachability for the inexperienced or those working alone, and actual utility for learning. I have stuck with it and have found it to be a good introduction to the subject.