What to read after INTRODUCTION TO ABSTRACT ALGEBRA FOR under graduate students?

 This book is a reference book for undergraduate introductory course in abstract algebra . It treats set theory, group theory, ring theory, and field theory, and Vector spaces. As an introduction, it presupposes no prior knowledge of abstract algebra, but provides a well-motivated, clear, and rigorous treatment of the subject, illustrated by many examples. Each of its chapters concludes with a variety of exercises ranging from the straightforward to the challenging in order to reinforce students' knowledge of the subject. Some of these are particular examples that illustrate the theory while others are general results that develop the theory further.