Algebra: Volume II

This book covers a whole lot of subjects in not-so-many pages. As someone pointed before, it is not intended as a first book on the subject. For one thing: there is not many examples on each topic, the exercises require you to really think and solve a problem, rather than introduce further easy examples to fix the concepts taught. My own experience is, I was puzzled first by the level of abstraction, and the lack of concrete examples on 'foreign' topics (at that time) was a little frustrating. Kind of "So what's the big deal with an ideal being principal or not? What's this all about?". After reading other, slower paced books on some of the same topics, van der Waerden becomes clear. I stringly recommend Elements of Number Theory and Elements of Algebra by John Stillwell, and Serge Lang's Linear Algebra (Undergraduate Texts in Mathematics) before attacking this one. That said, I do not regret buying this book at all. On the contrary, the first frustration became a strong motivation to complement it; and on the way I discovered a whole wonderful world.

I think there are few words to say about this book. This is a classic of Abstract Algebra very well known around the world among algebrists. This is a book that everybody interested about Algebra must read.

Great Quality. A book that will be in the bibliography of all algebra textbooks. Worth collection.

mathematically, this book is first rate. I turn to it when stuck on a passage in hungerford. However, this book shows its age in certain respects - e.g. category theory is completely snubbed - hence the index doesn't square well with a lot of the current standard terminology. Still, the fact that this book is in its seventh english printing says something about its value. It's like reading Dirac's principles of QM: sure, Griffiths is much easier, and exactly covers the standard undergrad subject matter -- but Dirac does it all in a third of the space, and with such brilliant clarity... Bottom line: don't buy this as your first algebra book, because it's old-fashioned. The point of reading a textbook is to get you far enough out there that you can read the current literature and be done with textbooks. But, if you already own Dummit and Foote (for undergrad material, lots of hand-holding in tough parts) and Lang or Hungerford (or even Herstein) for the standard first-year grad course perspective, this will round out your algebra library nicely.