The book has been designed for undergraduate and postgraduate students of Mathematics and it can also be used by those preparing for various competitive examinations. The text starts with an introduction to results from Sets and Number theory. It then goes on to cover Groups, Rings, Fields and Linear Algebra. Of late, Number theory has been becoming a part of Algebra syllabus and thus sufficient relevant material on the subject has been covered especially in the present edition. This includes besides others the phi, greatest integer and m?bius functions, primitive roots, Euler and Wilson theorems. The topics under Groups include subgroups, normal subgroups, finitely generated abelian groups, group actions, solvable and nilpotent groups. The course in ring theory covers ideals, embedding of rings, Euclidean domains, PIDs, UFDs, polynomial rings, Noetherian rings. Topics in Fields include algebraic extensions, normal and separable extensions, splitting fields, algebraically closed fields, Galois extensions and construction by ruler and compass. The portion on linear algebra deals with Vector spaces, linear transformations, eigen spaces, diagonalizable operators, inner product spaces etc. The theory has been strongly supported by numerous examples and worked out problems. There is also plenty of scope for the readers to try and solve problems on their own.