A Textbook of Abstract Algebra

Algebra is a branch of mathematics that uses mathematical statements to describe relationships between things that vary over time. These variables include things like the relationship between supply of an object and its price. When we use a mathematical statement to describe a relationship, we often use letters to represent the quantity that varies, since it is not a fixed amount. These letters and symbols are referred to as variables. The mathematical statements that describe relationships are expressed using algebraic terms, expressions, or equations. As it developed, algebra was extended to other non-numerical objects, like vectors, matrices or polynomials. Then, the structural properties of these non-numerical objects were abstracted to define algebraic structures like groups, ring, fields and algebras. This textbook presents a lucid and unified description of Abstract algebra at a level which can be easily understood by the students who posses reasonable mathematical aptitude and abstract reasoning. So that they can easily understand various mathematical concepts, techniques and tools needed for their course. Efforts have been made to explain such points in depth, so that students can follow the subject easily.