A concrete approach to abstract algebra Book

This is another excellent mathematics textbook written by WW Sawyer. If you would like to learn what Modern Algebra (or "Abstract Algebra") is about, this book starts from simple examples and builds up your intuition excellently. You understand why some axioms or properties are chosen for study, and how they can be used to enrich our understanding of number systems. I also thought the exercises were well crafted. The only complaint I have is that the the degree of a field extension was covered too quickly, and so was not clear to me until I consulted a different abstract algebra book. Other than that, I thought Sawyer clearly presented concepts, motivated them, and gave useful examples. He goes through the steps of examples, as well, which I often find as useful as the surrounding explanations.

The book is really an introduction to the subject, however, so if you want a full treatment of modern algebra, you will need to consult other texts.