Complex symplectic geometry with applications to ordinary differential operators

Complex symplectic spaces, and their Lagrangian subspaces, are defined in a ccord with motivations from Lagrangian classical dynamics and from linear o rdinary differential operators; and then their basic algebraic properties a re established. After these purely algebraic developments, an Appendix pres ents a related new result on the theory of self-adjoint operators in Hilber t spaces, and this provides an important application of the principal theor ems.