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Abstract Algebra is not a conceptually well-defined body of material, but a conventional name that refers roughly to one of the several lists of things thatAbstract algebra is essentially a tool for other branches of mathematics. ing them into algebraic problems, and then using the techniques of modern. Chapter 1 Why Abstract Algebra? History of Algebra. New Algebras. Algebraic Structures. Axioms and Axiomatic Algebra. Abstraction in Algebra. Chapter