Introduction * Manifolds and smooth structures * Lie group actions * Pseudogroups and groupoids * The standard momentum map * Generalizations of the momentum map * Regular symplectic reduction theory * The Symplectic Slice Theorem * Singular reduction and the stratification theorem * Optimal reduction * Poisson reduction * Dual Pairs * Bibliography * Index

* Winner of the Ferran Sunyer i Balaguer Prize in 2000.

* Reviews the necessary prerequisites, beginning with an introduction to Lie symmetries on Poisson and symplectic manifolds.
* Currently in classroom use in Europe.

* Can serve as a resource for graduate courses and seminars in Hamiltonian mechanics and symmetry, symplectic and Poisson geometry, Lie theory, mathematical physics, and as a comprehensive reference resource for researchers.