Introduction to Symplectic Geometry

This introductory book offers a unique and unified overview of symplectic geometry highlighting the differential properties of symplectic manifolds. It consists of six chapters:  Some Algebra Basics Symplectic Manifolds Cotangent Bundles Symplectic G-spaces Poisson Manifolds and A Graded Case concluding with a discussion of the differential properties of graded symplectic manifolds of dimensions (0n). It is a useful reference resource for students and researchers interested in geometry group theory analysis and differential equations.This book is also inspiring in the emerging field of Geometric Science of Information in particular the chapter on Symplectic G-spaces where Jean-Louis Koszul develops Jean-Marie Souriau's tools related to the non-equivariant case of co-adjoint action on Souriau’s moment map through Souriau’s Cocycle opening the door to Lie Group Machine Learning with Souriau-Fisher metric.