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Function Fields is a specialized category for books about the theory and applications of algebraic function fields — the study of fields of functions on algebraic curves and their arithmetic, geometry and Galois theory. Titles in this category range from graduate textbooks and research monographs that develop basic notions (Riemann–Roch, places/divisors, extensions and class field theory for global fields of positive characteristic) to computational guides and problem collections, as well as applied works linking function fields to coding theory, finite-field cryptography, explicit zeta and L-function calculations, and algorithmic number theory. Books here are aimed at advanced undergraduates, graduate students and researchers who want rigorous introductions, modern treatments, or specialized surveys connecting algebraic geometry, number theory and practical applications.

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