 Historically the term modern algebra came from the title of the first three editions of van der Waerden’s classic text of that name, renamed simply “Algebra” for its fourth edition in 1955. Volume 1 treated groups, rings, general fields, vector spaces, well orderings, and real fields, while Volume 2 considered mainly linear algebra, algebras (as vector spaces with a compatible multiplication), representation theory, ideal theory, integral algebraic elements, algebraic functions, and topological algebra. On the one hand modern algebra has since gone far beyond this curriculum, on the other this considerable body of material is already more than what can be assumed as common knowledge among graduating Ph.D. students in mathematics, for whom the typical program is too short to permit mastering all this material in parallel with focusing on their area of specialization.