Ring, subring, characteristic, ideals (maximal, prime, semiprime, principle), Quotient ring, integral domain, division ring and field, Ring homomorphism, Euclidean rings, Principal ideal domain, Unique factorization domain, Ring of polynomials, Field of quotients of integral domain, Field extensions. Finite field and extensions of fields.
Main Textbook: Contemporary Abstract Algebra, by J. A. Gallian, 8th edition, 2013. Subsidiary Books: Modern Algebra: An Introduction, by John R. Durbin, John Wiley & Sons, Inc. 3th edition, 2000.