Main subject categories: • Algebra • Groups and subgroups • Structure of groups • Homomorphisms and factor groups • Rings • Fields • Constructing rings and fields • Commutative algebra • Extension fields • Galois theoryA First Course in Abstract Algebra, 8th Editionretains its hallmark goal of covering all the topics needed for an in-depth introduction to abstract algebra – and is designed to be relevant to future graduate students, future high school teachers, and students who intend to work in industry. New co-author Neal Brand has revised this classic text carefully and thoughtfully, drawing on years of experience teaching the course with this text to produce a meaningful and worthwhile update. This in-depth introduction gives students a firm foundation for more specialized work in algebra by including extensive explanations of the what, the how, and the why behind each method the authors choose. This revision also includes applied topics such as RSA encryption and coding theory, as well as examples of applying Gröbner bases.