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Group theory books center on the study of symmetry via groups—sets equipped with a single operation satisfying associativity, identity, and inverses—and form a core part of abstract algebra. This category spans introductory texts covering permutations, cyclic and abelian groups, subgroups, homomorphisms, cosets and Lagrange’s theorem, normal and quotient groups, group actions, Sylow theorems, and basic classification ideas, as well as advanced works on representation theory, finite simple groups, and continuous structures like Lie and topological groups. Many titles blend rigorous proofs with problem sets and examples, and highlight applications to geometry, number theory, combinatorics, crystallography, physics, coding theory, and cryptography. The audience ranges from newcomers and undergraduates to graduate students and researchers, with offerings that are theoretical, computational, or historically oriented (e.g., Galois-inspired developments).

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