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Undergraduate Algebra is a text for the standard undergraduate algebra course. It concentrates on the basic structures and results of algebra, discussing groups, rings, modules, fields, finite fields, Galois Theory, and other topics. The author had also included a chapter on groups of matrices which is unique in a book at this level. Throughout the book, the author has attempted to strike a balance between abstraction and concrete results, providing illustrative examples to reinforce the general theory. Numerous exercises, ranging from the computational to the theoretical, have been added. In this second edition, some new topics have been included, such as Sylow groups, Mason's theorem on polynomials and the analogous abc conjecture over the integers, while other topics, including symmetric polynomials and field theory, have been expanded. Additionally, there are many new exercises of varying difficulty, and concrete examples of major unsolved problems in algebra, written in a language accessible to undergraduates, have been included to illuminate the vitality of mathematics.