Hamiltonian Reduction by Stages Background and the Problem Setting Symplectic Reduction Cotangent Bundle Reduction The Problem Setting Regular Symplectic Reduction by Stages Commuting Reduction and Semidirect Product Theory Regular Reduction by Stages Group Extensions and the Stages Hypothesis Magnetic Cotangent Bundle Reduction Stages and Coadjoint Orbits of Central Extensions Examples Stages and Semidirect Products with Cocycles Reduction by Stages via Symplectic Distributions Reduction by Stages with Topological Conditions Optimal Reduction and Singular Reduction by Stages by Juan Pablo Ortega The Optimal Momentum Map and Point Reduction Optimal Orbit Reduction Optimal Reduction by Stages. In this volume readers will find for the first time a detailed account of the theory of symplectic reduction by stages along with numerous illustrations of the theory. Special emphasis is given to group extensions including a detailed discussion of the Euclidean group the oscillator group the Bott Virasoro group and other groups of matrices. Ample background theory on symplectic reduction and cotangent bundle reduction in particular is provided. Novel features of the book are the inclusion of a systematic treatment of the cotangent bundle case including the identification of cocycles with magnetic terms as well as the general theory of singular reduction by stages.