"This textbook is an introduction to algebra via examples. The book moves from properties of integers, through other examples, to the beginnings of group theory. Applications to public key codes and to error correcting codes are emphasised. These applications, together with sections on logic and finite state machines, make the text suitable for students of computer science as well as mathematics students. Throughout the book, attention is paid to the historical development of mathematical ideas. This second edition contains new material designed to help students develop their mathematical reasoning skills as well as a new chapter on polynomials. The book was developed from first-level courses taught in the UK and USA, which proved successful in developing not only a theoretical understanding but also algorithmic skills. This book can be used at a wide range of levels: it is suitable for first- or second-level university students, and could be used as enrichment material for upper-level school students.