"The Theory of Groups is a branch of mathematics in which one does something to something and then compares the result with the result obtained from doing the same thing to something else, or something else to the same thing."
James R. NEWMAN, The World of Mathematics (1956)

Introduction to Modern Algebra

Introduction to Modern Algebra is likely the first course where you will see the notion of group. Not by chance this is done in such introductory course, since a group is the simplest algebraic object, the foundational structure in modern algebra. Although extremely simple structures, or maybe precisely because of their simplicity, groups can be the object of very refined constructions and they naturally appear in several areas of Mathematics (algebra, geometry, calculus) and Physics.