This book contains the basics of abstract algebra. In addition to elementary algebraic structures such as groups, rings and solids, Galois theory in particular is developed together with its applications to the cyclotomic fields, finite fields or the question of the resolution of polynomial equations. Special attention is paid to the natural development of the contents. Numerous intermediate explanations support this basic idea, show connections and help to better penetrate the underlying concepts. The book is therefore particularly suitable for learning algebra in self-study or accompanying online lectures.