Abstract algebra is the set of advanced topics of algebra that deal with abstract algebraic structures rather than the usual number systems. The most important of these structures are groups, rings, and fields. Important branches of abstract algebra are commutative algebra, representation theory, and homological algebra. Most students in abstract algebra classes have great difficulty making sense of what the instructor is saying. Moreover, this seems to remain true almost independently of the quality of the lecture. This book is based on the constructivist belief that, before students can make sense of any presentation of abstract mathematics, they need to be engaged in mental activities which will establish an experiential base for any future verbal explanation. No less, they need to have the opportunity to reflect on their activities. This approach is based on extensive theoretical and empirical studies as well as on the substantial experience of the authors in teaching abstract algebra. This text section is written in an informed, discussive style, closely relating definitions and proofs to the constructions in the activities. The book can also be used by those preparing for various competitive examinations. The text starts with a brief introduction to results from Set theory and Number theory. It then goes on to cover Groups, Rings, Fields and Linear Algebra. This book presents a lucid and unified description of Abstract algebra at a level which can be easily understood by the students who possess reasonable mathematical aptitude and abstract reasoning. The book provides an example oriented, less heavily symbolic approach to abstract algebra and the text emphasizes specifics such as rings, integral domains and field, polynomial rings, vector spaces, matrices and linear transformations etc. The book concludes with the coverage of eigen values and eigen vectors of matrices.