In the chapters on modern algebra in Advanced Algebra, different subjects in commutative and noncommutative algebra are covered. Additionally, the theory of associative algebras, homological algebras, algebraic number theory, and algebraic geometry are introduced.

There are numerous examples and hundreds of problems, along with tips or full solutions for the majority of the problems.

Every mathematician, whether pure or applied, aspiring or experienced, benefits from understanding the principles and methods in algebra that are carefully developed in Basic Algebra and Advanced Algebra. A comprehensive understanding of algebra and its place in all of mathematics is provided by the two texts taken together.

For the purpose of directing further research, the presentation comprises blocks of challenges that introduce new subjects and engineering and scientific applications. There are numerous examples, hundreds of problems, and a 90-page section containing suggestions or full solutions for the majority of the issues.