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Cyclotomic fields is a specialized mathematics book category focusing on the number fields obtained by adjoining roots of unity to the rationals; it covers their algebraic structure, Galois theory, arithmetic invariants (ring of integers, units, ideal class groups), and connections to class field theory, Iwasawa theory, and explicit reciprocity laws. Titles in this category range from introductory expositions and computational guides explaining cyclotomic polynomials and basic properties for advanced undergraduates to rigorous graduate-level and research monographs treating deep topics such as Kummer theory, the proof techniques behind results like early cases of Fermat’s Last Theorem, explicit class field constructions, and modern developments in p-adic L‑functions and modular forms. Books often include historical context (Gauss, Kummer), examples and explicit calculations, and prerequisites in algebra and number theory, making the category useful for students preparing for research as well as for researchers seeking reference material or computational methods.

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