This course gives an introduction of modern and abstract algebra to mathematics majors. Topics include the elementary theory of groups, binary operations, groups and subgroups, permutation groups, cosets and Lagrange's theorem, homomorphism and factor groups, and Sylow theory: an advanced topic in group theory. It also considers the elementary theory and definitions of rings and fields, integral domains, Fermat's and Euler's theorems, the field of quotients, rings of polynomials, homomorphisms and factor rings, and the basic theory of ideals.