Introduction to Modern Algebra was selected as a concise course of advanced algebra by Blue Zhong Yi of Peking University Publishing House. The book is handled by modern means and compiled by a famous mathematician and professor of mathematics at the University of California, Berkeley, to May Day. The higher education edition listed upstairs is the old edition of Peking University, which is seriously outdated and unclear in many places, while the Tongji edition is obviously insufficient.

In addition, we recommend two more difficult advanced algebra textbooks, Linear Algebra by HKUST Li Jiongsheng and Advanced Algebra by Tsinghua Zhang Xianke, which belong to the background research of Chinese Academy of Sciences. I suggest that you can try it if you are sure.