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I'm taking Beginning Arabic now and picked up this book to help me practice between classes. It's been invaluable in helping me "get" the script of a different writing system and I would recommend it to anyone starting to learn at home as well.
Edit: I've now worked my way through the beginning half of this book, the one that covers the basics of letters, numbers and other symbols (I am saving the second half, which covers more advanced Arabic, for when I take Arabic 2 next semester), and I stand by my initial comments. There are a few complicated concepts that my teacher had some difficulty explaining, and I found that reading about them in this book helped me more fully understand them, and also understand that most of them are also considered complicated by most people who are fluent Arabic speakers so it was no wonder I was confused! I've found the practice words and quizzes to be very helpful, and I really appreciate how clearly he explains pronunciation rules and the ways that some types of words are formed from root words or root consonants. I'd highly recommend this book as a starting point to anyone learning Arabic, though hopefully they would be able to use it in conjunction with an in-person way to practice writing and speaking it with a fluent speaker.
I already had a decent knowledge of the Arabic alphabet from Persian and pre-1917 Tatar, which use a subset of the original script used for Arabic. I have only dabbled in Arabic itself, and I picked this book up hoping to learn about some of the peculiarities of Arabic specifically, like tāʔ marbūṭa, and why final yāʔ sometimes represents /a/ and not /i:/. This book was helpful in answering my questions, and the presentation of the Arabic alphabet itself was complete just halfway through its 125 pages of so of content.
The book is more than that, however. The author wants the student to not only know the letters of the alphabet itself, but also be able to decipher street signs, country names in newspaper headlines, etc. This takes some preparation when the script infamously does not represent all the short vowels in the language. Thus, the reader gets a solid grounding in Arabic root structure so that when one is confronted with little more than the three- or four-letter consonant skeleton of an unfamiliar word, one can intuitively supply the vowels missing from the script. This is not quite a textbook of Arabic itself, but a linguistics-minded, independent student might find a proper textbook much smoother going after working through this book first.
The book dates from the late 1990s, and the one spot where it shows its age is in its insistence on teaching (and drilling) both handwriting forms and print forms from the very first lesson. I imagine that nowadays literacy in the Arabic world both for literate local people and foreign travelers is increasingly centered around the smartphone keyboard and display, so handwriting itself is less important for beginners.