For more than thirty years Modern Algebra has served the student community as a textbook for introductory courses on the subject. The book starts from set theory and covers an advanced course in group theory and ring theory. A detailed study of field theory and its application to geometry is undertaken after a brief and concise account of vector spaces and linear transformations. The last chapter discusses ring with chain conditions and Hibert@s famous theorem. The Eighth Edition is a distinctly improved version of the book incorporating new developments and thinking in the subject. Presentation of the subject matter has been vastly modified. Many results have been re-arranged, and the proofs of many results rewritten. Some more examples have been significant improvements have been made in presenting permutation groups, survey of some groups significant improvements have been made in presenting permutation groups, survey of some groups Galois extensions of fields more results have been added. A proof of the fundamental theorem of Galois extensions of fields more results have been added. A proof of the fundamental theorem of algebra has been included. In the theory of single linear transformation on a vector space, proofs of the results have been written with more details. Some results on diagonalization of matrices have also been added. The book is targeted to undergraduate and postgraduate levels.