In 1944, Edith Muller claimed that all the 17 wallpaper groups were found in Alhambra. Unfortunately, her paper only contained 11 of them. Grunbaum and Shephard found two more, and finally in 1987 Perez-Gomez found the missing four.

The book includes pictures and discussions of all the 17 wallpaper groups. Unfortunately, it does not include pictures of the "missing" patterns from Alhambra. For that you have to go to J.M. Montesinos: Classical Tessellations and Three-Manifolds.

This is a fantastic book in every way but one. Perseus Books has done such a terrible job printing it that I am returning my copy. It looks and feels worse than any book I have ever held in my hands. The paper is cheaper than any book I have on my shelf. I can see an empty spot in the glue on the binding. The text itself looks like a second generation photocopy.

All of this is a terrible disappointment to me, because everyone I have talked to has loved the content of the book, and I was expecting a good, strong paperback that I could keep for thirty years. This doesn't feel like it'll last thirty days. I can't recommend that anyone buy this book. Perhaps if you could get a cheap used copy it would be worth it, but sixty dollars? No. Get something else.

Some people believe that, for getting into algebraic geometry (by this I mean Grothendieck-like AG, with schemes and all that), one needs a monolithic training in commutative algebra (something like both volumes of Zariski-Samuel, for example). I disagree. This little book seems to be specially suited to those who want to learn AG. It's a bit too brisk, specially at the beginning - if you don't already have an acquaintance with the basics of groups, rings and ideals, you may run into trouble - but very illuminating. Masterful choice of topics, great exercises (as a matter of fact, about half the topics of the book, and more specifically the ones that are directly related to AG, are treated in the exercises, some of them quite challenging) - like one said before, it looks like a "chapter 0" of Hartshorne's book on AG. The authors consciously estabilish relations between the commutative algebra and the modern foundations of AG over and over along the way, illuminating both topics.

For the algebra itself, it also gets on well with Rotman's "Galois Theory" and MacDonald's out-of-print introduction to AG, "Algebraic Geometry - Introduction to Schemes", besides being the perfect preamble in commutative algebra to the books of Mumford and Hartshorne. A gem.

This is how mathematics texts SHOULD be written. As in technical writing, the smaller text is the better written text. Everything is clean and direct, with clairity obviously a prime consideration. One never gets mired down. The proofs are always as close to a "THE BOOK" proof as possible, with illuminating examples, and plenty of excercises, many with outlines for solution, which makes the book ideal for self study. This book is a revelation. If I had to take only one math text with me to a desert island, this would be the one.