Symplectic geometry

Question

I'm very interested in studying symplectic geometry which is compulsory in hamiltonian mechanics but sadly I just can't find a appropriate book to do that.Would anyone be helpful enough to indicate a clue?

Answer 1

The following are two good introductions to the subject.

Ana Cannas da Silva:Lectures on symplectic geometry, Springer Lecture Notes in Mathematics 1764.

Rolf Berndt: An introduction to symplectic geometry, AMS Graduate Studies in mathematics 26.

Answer 2

If you are interested in Symplectic Geometry aiming at Hamiltonian Mechanics you can take a look to

1) Hofer and Zehnder's "Symplectic Invariants and Hamiltonian Dynamics" (Birkhäuser)

2) Abraham and Marsden's "Foundations of Mechanics" (Addison-Wesley Publishing Company) is a formidable book about Classical Mechanics but introduces rigorously all the needed Geometry (Differentiable Manifolds, Symplectic Manifolds, Lie Groups etc).