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The book contains topics as per the model syllabus of the University Grants Commission (UGC), India for a course an algebra and linear algebra and suitable for under graduate and post graduate students of mathematics. The book has been made self-contained with a preliminary chapter on set theory which also forms a part of the course. Besides set theory, the book contains topics like integer, groups, rings and fields, polynomial, vector spaces, linear transformation, matrices and Boolean Algebra.The book is written in a simple and lucid manner with examples and applications so that the students can enjoy the applications of abstract topics to number theory and theory of equations (roots of polynomials). Finally it contains an additional chapter on fuzzy set theory.