I agree with the other reviewers: this is a very good resource with decent explanations, progression, chapter delineation, and all the rest. It does not teach script though, so beware you will need to know and be familiar with Arabic script.
However something that I found very frustrating was that despite being a learner's book the vowelling was rarely present in the activities which if you don't have a photographic memory means you will be looking in a dictionary often which slows you down and interrupts you, something that I did not expect given the on the face of it well designed vocabulary progression. In addition, frequently new words are introduced into the exercises without vowelling or prior introduction which I found a frustrating editorial error, showing perhaps that while Arabic speakers and professionals may have looked at it, actual learners have not! Other reviewers may disagree, but I do not subscribe to old-fashioned views on language teaching that like inconveniences such as putting all the vocabulary in the back of the book in a glossary instead of with the text that think such things are good to 'encourage' you to learn the vocabulary. There is no glossary to this book either, another flaw I feel that hampers progress through the book that could have easily been added. As such I felt the vowelling was inconsistent, sometimes it was there and sometimes it wasn't. Maybe it's not much, but I found it very annoying while going through the book. McGraw Hill Arabic Verbs & Essentials of Grammar has no such problems for presenting the essentials, though it has no exercises unfortunately, always very important.
As a final note, it does not contain all the necessary elements of Arabic grammar, but I won't mark it down for that, since that is probably outside the purview of such an introductory work.
I still recommend this text as an introduction that no doubt has no betters on the market, but get a good dictionary. Good online Arabic dictionaries don't seem to exist.