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.