Various articles of Kaledin might be interesting.
Appendix 4.7 of Felix, Oprea, Tanre in Homotopy th folder: Basic Hermitian and symplectic linear algebra, and basic notions of complex structures
Different faces of geometry, ed Donaldson, Eliashberg, Gromov. Contains some possibly useful survey articles.
http://sbseminar.wordpress.com/2012/01/09/what-is-a-symplectic-manifold-really/
http://sbseminar.wordpress.com/2012/01/14/why-do-symplectic-manifolds-need-to-be-closed/
Symplectic geometry: See various things in Symplectic folder
nLab page on Symplectic stuff