Basic Algebra and its companion volume Advanced Algebra systematically develop concepts and toolsin algebra that are vital to every mathematician, whether pure or applied, aspiring or established. These two books together aim to give the reader a global view of algebra, its use, and its role in mathematics as a whole. The idea is to explain what the young mathematician needs to know about algebra in order to communicate well with colleagues in all branches of mathematics. The books are written as textbooks, and their primary audience is students who are learning the material for the first time and who are planning a career in which they will use advanced mathematics professionally. Much of the material in the books, particularly in Basic Algebra but also in some of the chapters of Advanced Algebra, corresponds to normal course work. The books include further topics that may be skipped in required courses but that the professional mathematician will ultimately want to learn by self-study. The test of each topic for inclusion is whether it is something that a plenary lecturer at a broad international or national meeting is likely to take as known by the audience.