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"Elliptic curves" as a book category covers literature focused on the theory and applications of elliptic curves—smooth projective cubic curves with a group law—primarily within number theory and algebraic geometry but also in cryptography, computational mathematics, and arithmetic geometry. Books in this category range from introductory texts explaining basic concepts (Weierstrass equations, group law, rational points, torsion, and reduction) and computational techniques to advanced monographs treating deep topics such as the Mordell–Weil theorem, Galois representations, modularity, L-functions and the Birch–Swinnerton-Dyer conjecture, as well as practical guides to elliptic curve cryptography, algorithms, and software. Typical readers are undergraduates with algebra background, graduate students, and researchers; many titles cross-list with algebraic geometry, number theory, and cryptography and may assume familiarity with commutative algebra, complex analysis, or computational number theory.

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