This Fourth Edition of Introduction to Abstract Algebra is a self-contained introduction to the basic structures of abstract algebra: groups, rings, and fields. This book is intended for a one or two semester abstract algebra course. The writing style is appealing to students, and great effort has been made to motivate and be very clear about how the topics and applications relate to one another. Over 500 solved examples are included to aid reader comprehension as well as to demonstrate how results in the theory are obtained. Many applications (particularly to coding theory, cryptography, and to combinatorics) are provided to illustrate how the abstract structures relate to real-world problems. In addition, historical notes and biographies of mathematicians put the subject into perspective. Abstract thinking is difficult when first encountered and this is addressed in this book by presenting concrete examples (induction, number theory, integers modulo n, permutations) before the abstract structures are defined. With this approach, readers can complete computations immediately using concepts that will be seen again later in the abstract setting. Special topics such as symmetric polynomials, nilpotent groups, and finite dimensional algebras are also discussed.