A First Course in Abstract Algebra

Rotman's book is a standard for first courses in Abstract Algebra. The book is easy to read and includes plenty of problems to work on. He even includes several standard syllabi in the preface, depending on the type of course that may be taught with it. It begins with some number theory, then goes into the traditional group and ring concepts. The only reason I would say to not buy this book is if you really don't like the theorem-proof, theorem-proof kind of writing, but if you don't, you're likely not interested in Abstract Algebra anyway. An excellent book for learning as well as reference.

This is an excellent bookto use fo an introduction to modren algebra. It is clear and very accessible, with many useful examples. I highly recommend it.