I can only summarize what other customers have already said about this book. The test problems are really different from those that ETS itself hands out and those of the (unfortunately single) test exam in "Cracking the GRE Math Subject Test". Worse is that often the knowledge that is asked is not required for the real test, more intricate and neither covered in the "review" nor in the explanation of the correct answer.
However it is the only book, that provides a sufficient number of full-length practice exams with a look-and-feel which is similar to that of a GRE subject test, therefore I still give it a 3 out of 5.

First, many of the types of questions in the 6 practice exams are pointless to study, since you won't encounter anything remotely resembling them on the real GRE. Second, the explanations of the solutions are rarely satisfactory. Third, the review section is a complete joke and, like the questions in the practice exams, many of the topics it covers are completely worthless with regards to the GRE (e.g. cubic spline interpolation, fourier series). I didn't read the review section very thoroughly (though I did glance over subtitles, so I know that a lot of time-wasting material was included), but what I did look at in some depth was poorly explained.
All of this said, the book isn't entirely useless. If you use it as a companion to a better GRE prep book (cracking the GRE) and have a discerning eye for what will and won't be necessary to study, it does offer some good review questions if you have time to weed through it.

All in all the product was a decent review of the math covered by the GRE math subject test, but the format of the practice tests is not at all in line with the version that ETS has on their website. As far as I can tell, ETS doesn't ask you ugly computational problems which is all these tests are. Use the review section to remind yourself of the most prevalent theorems and do some of the test problems to review the computations. But don't use your results from these practice tests to make any prediction about your real score on test day. There is no way ETS would expect you to finish a test of this style in under 3 hours. That would just not be feasible.

The level of difficulty and depth of the questions in this book is generally much higher than the real exam. While studying questions that are modestly harder than the actual test is often a good way to score high, this book goes well beyond that level, to the point of being almost useless.

The proofreading of this book is remarkably poor. Several problems have incorrect solutions. Such inaccuracies (as well as many typos) leave a reader wondering whether any of the content can be trusted.

The typesetting is also very poor. While this is primarily a cosmetic issue, in some places it makes the content less comprehensible.

The book summaries the main topics very briefly. This make the summary a bit useless (it's more like a formula sheet with all the theorems/lemmas than something you can learn of...). On the other hand, the book contains six fully solved practice tests. The practice tests level are much higher than the real GRE Math level, but still, it is a good way to learn for the exam.
I would recommend buying this book with "Cracking the GRE Math Test" by the Princeton Review which has a much better summary of the main topics.

The material covered in this text is actually much more difficult and frankly ridiculous than what's actually covered in the subject gre. The book includes problems with complicated substitutions, series, etc. and does not present an accurate representation of the test, which from my experience seemed much simpler and would be better studied for by reviewing old class notes and problems.

The material covered in this text is actually much more difficult and frankly ridiculous than what's actually covered in the subject gre. The book includes problems with complicated substitutions, series, etc. and does not present an accurate representation of the test, which from my experience seemed much simpler and would be better studied for by reviewing old class notes and problems.

I know one of the authors of this book, and therefore have a bit of insight as to his intentions. He did not write the questions by going through volumes of old GRE questions and changing numbers slightly, ensuring they would be nearly identical to the actual GRE. Rather, he prepared a set of questions, (nearly) all of which competent mathematics students should be able to solve. Admittedly, the problems are more difficult than actual exam questions, but that is probably the best way to train-- athletes run with weights, swing heavier bats when practicing-- why not mathematicians?

The other option (Princeton Review) is presented in a much 'nicer' way and its coverage is much closer to the actual examination. Many of the questions, however, are a bit too easy, and students who use it as a sole source of test questions may well be in for a surprise come exam time.

Bottom Line: If you want to get into a good graduate school, it wouldn't hurt to buy either of the aforementioned books. Each hads its strengths, and you can never go wrong with more problems. The only source one should use to gauge the difficulty of the actualy exam is the sample GRE (available for free online).

A final note: As other reviewers have noted, the book is saturated with errors. It's almost incomprehensible that REA continues to republish the book without editing it, but they don't seem to care. The errors may be annoying, but they're usually easy to fix and won't interfere with the reading of the book (with the exception of erroneous solutions).

Let me first say that I have the 1997 printing. From what I can see, very little seems to change from printing to printing, so I'm assuming that most of my complaints from this printing still hold for a "newer" edition that you buy now.

Many reviewers have pointed out that the practice tests in this volume are harder than the actual GRE math subject test, which I found to be true. It's not that this is, a fortiori, a bad thing; sometimes training on harder tests makes the real thing seem much easier in contrast. However, the practice tests in this book are not just harder than the actual test, but quite different in terms of the skill set they seem to require. So if you practice from this book, you're really not practicing the types of questions you'll see on the GRE.

More specifically, there are plenty of questions in the REA book that require odd leaps of intuition that even the more seasoned mathematician is not likely to make, at least not without a lot of time to sit down and play with the problem. (Of course this is an impossibility given the tight schedule they give you on the real exam to answer 66 questions!)

As an example (and this is a bit rough since it's not easy typing up math expressions like this):

SUM (from 1 to m) arctan( 1 / ( n^2 + n + 1 ) )

I won't detail the contorted series of substitutions and simplifications the answer key suggests. Perhaps I'm being naive, but I'm in my fifth year of graduate study and I have never come across a problem like this on a timed test. This is more like the kind of brain-teaser you might find in one of the common math journals. (Think Putnam exam problem, but not really as difficult.) Needless to say, the real test does not require this kind of reasoning. Everything on the real test suggests to the well-prepared student a reasonably standard method of attack.

Unfortunately, there are a lot of these useless practice problems. They are a distraction, especially when you want to time yourself and take a full practice test. (It's easy enough to skip these when casually working problems.) It's also distracting to find questions covering relatively obscure topics. Like, what is Green's function for a 2nd order differential equation? (I guess the solution guide "explained" it to me.) I've taught differential equations from multiple books for years and I've never seen it. I'm sure somebody covers in it their curriculum, but can we really expect that everyone should know how to compute Green's function?

A lot has been said as well about typos. Again, perhaps I am wrong about the new edition, but I suspect many of these remain. Worse than the typos for me was the typesetting. In this, the modern age of technology, why, I ask, does this book still look like it was produced on a typewriter? We've had TeX for many years now, for crying out loud! A few of my favorite typographic blunders:

In a discussion of continuity, an appropriate looking epsilon symbol appears, and then in the very same line, the symbol for element inclusion in a set (which sort of looks like an e I guess) plays the role of the very same epsilon. Later in the book, the epsilon symbols reappears, but now used as element inclusion.

In another solution, the Greek letter alpha appears, and then suddenly turns into the symbol for "proportional to"--only vaguely resembling an alpha in the most superficial of characteristics--again in the very same line.

The most unforgivable offense is the following "computation" of the number non-isomorphic abelian groups of order 40:

The answer according to REA? Seven. Here's their explanation:

"Non-isomorphic abelian groups of the same order, n, are effectively the direct products Z_n1 X Z_n2 X ... X Z_nk where n_1 x n_2 x ... n_k = n and each n_i is a divisor of n. In this case, the products yielding 40 are 40, 10 x 4, 8 x 5, 20 x 2, 10 x 2 x 2, 5 x 4 x 2, and 5 x 2 x 2 x 2."

Huh!?! I'm pretty sure the answer is three. The very elementary theorem from your first abstract algebra course states:

Z_m = Z_m1 X Z_m2 iff m1 and m2 are relatively prime.

Hence,

Z_40 = Z_8 X Z_5

Z_10 X Z_4 = Z_5 X Z_2 X Z_4 = Z_20 X Z_2

Z_10 X Z_2 X Z_2 = Z_5 X Z_2 X Z_2 X Z_2

Yup. Three isomorphism classes, not seven. Heaven help the poor sap who uses this book to "remember" the facts long ago forgotten.

I admit, truly egregious errors like this are rare. But little slips, typos, errors, and miscalculations abound, all laid out in ugly, ugly typeface.

It's a shame. There are so few resources out there to help students practice for this test. The ETS book is great, but it has no detailed solutions; only the answer key.

Oh, yeah, and the math review that occupies the first half ot this tome? It sucks too.

I think the book is good, hoever, I do not finish reading it, that's why I did not rate it "5".

By the way, I think your worker in China do not take his job seriously. When I was not at home, he simply put the book on the floor leaning the door. It was easily picked by others, and I could have no chance to get it back.