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This textbook is designed for the UG/PG students of mathematics for all universities over the world. It is primarily based on the classroom lectures, the authors gave at the University of Delhi. This book is used both for self-study and course text. Full details of all proofs are included along with innumerous solved problems, interspersed throughout the text and at places where they naturally arise, to understand abstract notions. The proofs are precise and complete, backed up by chapter end problems, with just the right level of difficulty, without compromising the rigor of the subject. The book starts with definition and examples of Rings and logically follows to cover Properties of Rings, Subrings, Fields, Characteristic of a Ring, Ideals, Integral Domains, Factor Rings, Prime Ideals, Maximal Ideals and Primary Ideals, Ring Homomorphisms and Isomorphisms, Polynomial Rings, Factorization of Polynomials, and Divisibility in Integral Domains.