This volume presents the foundations of the theory of moduli of algebraic curves over the complex numbers. The first volume focused on the geometry of a fixed smooth curve, while this volume explores the global moduli space of stable curves. The main purpose is to provide a comprehensive and detailed foundation for the theory of moduli of algebraic curves, incorporating multiple perspectives: algebraic-geometric, complex-analytic, topological, and combinatorial. The book includes a contribution by Joseph D. Harris, and covers topics such as the Hilbert scheme, nodal curves, deformation theory, Kuranishi families, and the moduli space of stable curves. It also discusses line bundles on moduli, the projectivity of the moduli space, Teichmüller theory, smooth Galois covers of moduli spaces, cycles on moduli spaces, and the intersection theory of tautological classes. The book also includes a detailed treatment of Brill–Noether theory and the study of linear series on moving curves. The text is structured to provide a self-contained introduction to the theory of stacks and moduli spaces, with a focus on the construction of the moduli space of stable curves and its properties. The book also includes a guide for the reader, a list of symbols, and a bibliography. The main results include the proof of the projectivity of the moduli space of stable curves, the study of the tautological ring, and the application of Kontsevich's proof of Witten's conjecture. The book is intended for researchers and graduate students in algebraic geometry and related fields.This volume presents the foundations of the theory of moduli of algebraic curves over the complex numbers. The first volume focused on the geometry of a fixed smooth curve, while this volume explores the global moduli space of stable curves. The main purpose is to provide a comprehensive and detailed foundation for the theory of moduli of algebraic curves, incorporating multiple perspectives: algebraic-geometric, complex-analytic, topological, and combinatorial. The book includes a contribution by Joseph D. Harris, and covers topics such as the Hilbert scheme, nodal curves, deformation theory, Kuranishi families, and the moduli space of stable curves. It also discusses line bundles on moduli, the projectivity of the moduli space, Teichmüller theory, smooth Galois covers of moduli spaces, cycles on moduli spaces, and the intersection theory of tautological classes. The book also includes a detailed treatment of Brill–Noether theory and the study of linear series on moving curves. The text is structured to provide a self-contained introduction to the theory of stacks and moduli spaces, with a focus on the construction of the moduli space of stable curves and its properties. The book also includes a guide for the reader, a list of symbols, and a bibliography. The main results include the proof of the projectivity of the moduli space of stable curves, the study of the tautological ring, and the application of Kontsevich's proof of Witten's conjecture. The book is intended for researchers and graduate students in algebraic geometry and related fields.