Abstract Algebra is part of the new AMS series of Pure and Applied Undergraduate Texts. The book is well written and concise. Unlike in most algebra texts, the subject is introduced through a series of examples and connections to other fields of mathematics are often drawn. In many places, the author makes a point to provide historical context. The many exercises are spread throughout the sections and build on one another. In many respects, the book has a “learning by discovery” feel. It is designed so that an instructor would have enough amount of time to get to Galois theory in a one semester course.
Instructors should make sure that this book would be a good fit for their classroom. It is written for a one-semester or one-year course in undergraduate level algebra. The text introduces the algebra needed to move from one chapter to the next, but does not outline all of the traditional algebra techniques and concepts. It does not intend to prepare students for graduate study. For most departments, the majority of whose students do not attend graduate school, this book could be very useful.
Overall, I think the text is written well and fulfills the goal for which it is intended. As an Assistant Professor at a teaching-focused small liberal arts institution, I am interested in using the text in my own classroom.
Michael Rowell is an Assistant Professor of Mathematics at Pacific University. His research interests are in Combinatorics and Number Theory. His website is www.math.pacificu.edu/~rowell and his email is firstname.lastname@example.org.