A Concrete Approach to Abstract Algebra: From the Integers to the Insolvability of the Quintic, Second Edition provides a primer and reference on abstract algebra for readers whose interests lie in mathematics and information and physical sciences. Adopting the unique 'rings first' approach, the work provides a gentle transition into abstract structures that will make abstract algebra more natural to interested readers. In addition to introducing the major concepts of modern algebra, the book covers numerous applications which are intended to illustrate the concepts and convince the reader of the utility and relevance of algebra today. This Second Edition features 40% new or revised content, including complete and self-contained proofs of the fundamental theorems of algebra and the Insolvability of the Quintic, and new coverage of commutative rings and linear transformations. Offers an extraordinarily diverse reference of the algebraic field providing foundational progression through algebraic concepts suitable for newcomers and experts alike Demonstrates in simple language-using multiple examples and exact proofs-how most concepts within abstract algebra are actually tools used to solve difficult, but well-known problems Employs a gradual approach to build on relatively familiar material (integers, polynomials) Explores more abstract topics while providing the classical approach of introducing groups first as automorphisms Supports both prospective graduate students as well as prospective teachers.