This introduction to modern or abstract algebra addresses the conventional topics of groups, rings, and fields with symmetry as a unifying theme, while it introduces students to the active practice of mathematics. Its accessible presentation is designed to teach students to think things through for themselves and change their view of mathematics from a system of rules and procedures, to an arena of inquiry. The text provides plentiful exercises that give students the opportunity to participate in and investigate algebraic and geometric ideas which are interesting, important, and worth thinking about.