This is a comprehensive treatment of basic parts of abstract algebra. Starting from scratch, the authors gradually present fundamentals of the classical theory of groups, rings, fields and polynomials. Then they proceed to Galois theory and its applications to ruler and compass constructions. The book also contains basics on linear codes, and an introduction to representation theory of groups. The presentation is clear and detailed. Moreover, there are numerous examples and exercises of varying levels of difficulty accompanying each chapter. The book ends with an interesting chapter on the history of algebra. Material presented here has been chosen in such a way that it includes a complete (abstract) algebra course on the 'bachelor' level taught at European universities. It has been field-tested by its use in the Erasmus educational project in past years. The experience of the authors together with a careful presentation of material makes this book a valuable addition to modern textbooks in algebra.