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High Quality Content by WIKIPEDIA articles! Algebra is one of the main branches of mathematics, and concerns the study of structure, relation and quantity. It studies the effects of adding and multiplying numbers, variables, and polynomials, along with their factorization and determining their roots. In addition to working directly with numbers, algebra also covers symbols, variables, and set elements. Addition and multiplication are general operations, but their precise definitions lead to structures such as groups, rings, and fields.