Crainic M., Fernandes R.L., Mărcuţ I. Lectures on Poisson Geometry

American Mathematical Society, 2021. — 503 p. — (Graduate Studies in Mathematics 217). — ISBN 9781470464301.This excellent book will be very useful for students and researchers wishing to learn the basics of Poisson geometry, as well as for those who know something about the subject but wish to update and deepen their knowledge. The authors' philosophy that Poisson geometry is an amalgam of foliation theory, symplectic geometry, and Lie theory enables them to organize the book in a very coherent way. ―Alan Weinstein, University of California at Berkeley This well-written book is an excellent starting point for students and researchers who want to learn about the basics of Poisson geometry. The topics covered are fundamental to the theory and avoid any drift into specialized questions; they are illustrated through a large collection of instructive and interesting exercises. The book is ideal as a graduate textbook on the subject, but also for self-study. ― Eckhard Meinrenken, University of TorontoBasic Concepts
Poisson Brackets
Poisson Bivectors
Local Structure of Poisson Manifolds
Poisson Geometry Around Leaves
Symplectic Leaves and the Symplectic Foliation
Poisson Transversals
Symplectic Realizations
Dirac Geometry
Submanifolds in Poisson Geometry
Global Aspects
Poisson Cohomology
Poisson Homotopy
Contravariant Geometry and Connections
Symplectic Groupoids
Complete Symplectic Realizations
A Crash Course on Lie Groupoids
Symplectic Groupoids
Appendices
Appendix A. Lie Groups
Appendix B. Symplectic Structures
Appendix C. Foliations
Appendix D. Groupoids: Conventions and Choices