The practice of algebraic curves : a second course in algebraic geometry / David Eisenbud and Joe Harris.

Includes bibliographical references and index.

Plane algebraic curves -- Divisors and linear systems -- Projective varieties -- Morphisms and rational maps -- Riemann-Roch theorem -- Singularities and normalization -- Intersection theory -- Moduli of curves -- Brill-Noether theory -- Computational methods and examples.

This advanced graduate-level textbook provides a comprehensive introduction to algebraic curves and modern algebraic geometry through a strongly example-driven and computational approach. Building upon foundational ideas in algebra, geometry, and topology, the book develops the theory of plane curves, divisors, linear systems, projective varieties, and morphisms while emphasizing geometric intuition and practical techniques. The authors systematically introduce core concepts such as singularities, normalization, intersection multiplicities, Riemann-Roch theory, moduli spaces, and Brill-Noether theory, illustrating how abstract algebraic methods can be applied to concrete geometric problems. Numerous worked examples, exercises, and computational perspectives help readers understand both the classical and modern aspects of algebraic geometry. Designed for graduate students and researchers, the work serves as a second course in algebraic geometry and an accessible bridge to advanced research literature in algebraic and arithmetic geometry.