Moderne Algebra

Moderne Algebra is a two-volume German textbook on graduate abstract algebra by Bartel Leendert van der Waerden (1930, 1931), originally based on lectures given by Emil Artin in 1926 and by Emmy Noether (1929) from 1924 to 1928. The English translation of 1949–1950 had the title Modern algebra, though a later, extensively revised edition in 1970 had the title Algebra.

The book was one of the first textbooks to use an abstract axiomatic approach to groups, rings, and fields, and was by far the most successful, becoming the standard reference for graduate algebra for several decades. It "had a tremendous impact, and is widely considered to be the major text on algebra in the twentieth century."^[1]

In 1975 van der Waerden described the sources he drew upon to write the book.^[2]

In 1997 Saunders Mac Lane recollected the book's influence:^[3]

• Upon its publication it was soon clear that this was the way that algebra should be presented.
• Its simple but austere style set the pattern for mathematical texts in other subjects, from Banach algebras to topological group theory.
• [Van der Waerden's] two volumes on modern algebra ... dramatically changed the way algebra is now taught by providing a decisive example of a clear and perspicacious presentation. It is, in my view, the most influential text of algebra of the twentieth century.