"...The present book offers a thorough description of [reduction] theory and a unified treatment of most of its developments and generalizations, with a particular emphasis on those due to the authors. It contains many important results which cannot be found in other books, and covers a large part of the recent developments related to momentum maps and reduction. This book fills a need and will be appreciated by specialists as well as by persons new to the field..." -MATHEMATICAL REVIEWS

• 1 Manifolds and Smooth Structures.- 2 Lie Group Actions.- 3 Pseudogroups and Groupoids.- 4 The Standard Momentum Map.- 5 Generalizations of the Momentum Map.- 6 Regular Symplectic Reduction Theory.- 7 The Symplectic Slice Theorem.- 8 Singular Reduction and the Stratification Theorem.- 9 Optimal Reduction.- 10 Poisson Reduction.- 11 Dual Pairs.

"...The present book offers a thorough description of [reduction] theory and a unified treatment of most of its developments and generalizations, with a particular emphasis on those due to the authors. It contains many important results which cannot be found in other books, and covers a large part of the recent developments related to momentum maps and reduction. This book fills a need and will be appreciated by specialists as well as by persons new to the field..." -MATHEMATICAL REVIEWS

• 1 Manifolds and Smooth Structures.- 2 Lie Group Actions.- 3 Pseudogroups and Groupoids.- 4 The Standard Momentum Map.- 5 Generalizations of the Momentum Map.- 6 Regular Symplectic Reduction Theory.- 7 The Symplectic Slice Theorem.- 8 Singular Reduction and the Stratification Theorem.- 9 Optimal Reduction.- 10 Poisson Reduction.- 11 Dual Pairs.

"...The present book offers a thorough description of [reduction] theory and a unified treatment of most of its developments and generalizations, with a particular emphasis on those due to the authors. It contains many important results which cannot be found in other books, and covers a large part of the recent developments related to momentum maps and reduction. This book fills a need and will be appreciated by specialists as well as by persons new to the field..." -MATHEMATICAL REVIEWS

• 1 Manifolds and Smooth Structures.- 2 Lie Group Actions.- 3 Pseudogroups and Groupoids.- 4 The Standard Momentum Map.- 5 Generalizations of the Momentum Map.- 6 Regular Symplectic Reduction Theory.- 7 The Symplectic Slice Theorem.- 8 Singular Reduction and the Stratification Theorem.- 9 Optimal Reduction.- 10 Poisson Reduction.- 11 Dual Pairs.