Abstract algebra got a good start at the end of19th century and has developed into one of the important pillars of modern mathematics, including group theory, domain theory and ring theory. Because of its generality and the basic nature of its methods and results, it has penetrated into different fields of mathematics and exerted an important influence on the development of modern mathematics. Group theory is one of the important parts of abstract algebra and the foundation of abstract algebra. Abstract field theory was first studied by Weber in 1893. The algebraic theory of field theory put forward by Steinitz in 19 10 laid the foundation of field theory and became an important milestone in the development of abstract algebra. Rings and ideal structures can be found in the last century, but abstract theory is the product of this century. Nott made a very profound study of rings and ideals, and made a systematic theory of rings and ideals in 1926. This summative work marks the birth of abstract algebra. Vander Waals Deng's book Algebra is a systematic summary of Nott, Anting and his own work, and it is a sign of the maturity of abstract algebra, so it has become a classic for learning abstract algebra. Since then, great progress has been made in the study of abstract algebra.