This is a reprint of the 1965 edition. This book was originally a two volume set. It's now a large 818-page, unwieldy paperback in the narrow format of Dover reprints. (Don't get me wrong I love Dover reprints, this one is just too thick for the format). The second half from page 512 on is all that is worth while anyway. This book is very pendantic in the worse "New Math" sense (circa 1960). Meaning it emphasizes arbitrary abstract axioms, lacks historic perspective, concrete examples and real world applications; and, much is left to the reader as exercises. This is a shame since Modern Algebra is rich in history and application. The pedantic pretensions don't stop there. The book uses the number theorem approach to proofs without mentioning their common names (Since history is completely absent, this isn't a surprise). This is NOT a standard reference today, if it ever was in the past. Memorizing the theorem numbers will do you no good in your coffee shop conversations. The book only gets interesting in it's latter half, it's too bad you have to lug the first 500 pages along for the ride. Adding insult to pedantry, the really interesting parts are left as exercises! That's ok if you're paying big bucks for a professor and a TA to help you along, but as a self-study book, it's down right annoying. If you're looking for an introduction, I'd recommend Herstein's Topics in Algebra or Birkoff & MacLane's Survey over this one. If you're looking for more advanced treatment, I'd recommend Van der Waerden's Modern Algebra or Jacobson's Lectures in Abstract Algebra. These come in multi-volume sets that making reading easier. I'm sure there are better current books on the subject, but I'm not familiar enough to make a recommendation. I can only dissuade you from purchasing this one as your only reference or an intro.

Hard reading at times but worth the money. Get Durbin's "Modern Algebra" if you can afford it. Despite what some other reviewers are saying the exercises alone validate buying the book. CONTENTS: ALGEBRAIC STRUCTURES (sets,isomorphism in general, groups, an embedding theorem), NEW STRUCTURES FROM OLD (equivalence relations, quotient structures, some isomorphism theorems), THE NATURAL NUMBERS, RINGS AND FIELDS, VECTOR SPACES, POLYNOMIALS, REAL AND COMPLEX NUMBERS (constructions), ALGEBRAIC EXTENSIONS OF FIELDS (Galois Theory), LINEAR OPERATORS, INNER PRODUCT SPACES (Spectral Theorem), AXIOM OF CHOICE.

This book has received much undue criticism from other reviewers. Yes, the book is too thick (should be two volumes) and a bit old. But consider this:

I've self-taught myself most of this book in the past year, while attending school full-time as a materials science major (a whole field known to shy away from mathematics).

This book is unbelievably affordable and covers most of the main topics of modern algebra (good enough for those of us who just want to learn basics).

The book is entirely self-contained, which helps a lot if you don't have the most extensive mathematics background.

If your discipline isn't math but you're tired of "learning," ie. skirting around mathematical topics, in your classes, check out this book.