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2 Typos fixed

First,we

First, we recall that symplectic manifold is a smooth manifold, M, $M$, equipped with a closed nondegenerate differential 2-form, $\omega$, called the symplectic form. The study of symplectic manifolds is called symplectic geometry.In h$\ddot{o}$rmander's geometry. In Hörmander's classic book ALPDO(The ALPDO (The analysis of partial differential operatorsⅠ-Ⅳ )，he wroted：symplectic operators -Ⅳ) he wrote: symplectic geometry pervades a large part of the modern theory of linear partial differential operators with variable coefficients.And coefficients. And he had devoted the entire chapter ⅩⅩⅠto ⅩⅠ to discuss it.

Now,with

Now, with some basic background (its origins in the Hamiltonian formulation of classical mechanics) mechanics), I want to know further that why it would make such a important role in modern analysis (such as fourier integral operators) operators)?

First,we recall that symplectic manifold is a smooth manifold, M, equipped with a closed nondegenerate differential 2-form, $\omega$, called the symplectic form. The study of symplectic manifolds is called symplectic geometry.In h$\ddot{o}$rmander's classic book ALPDO(The analysis of partial differential operatorsⅠ-Ⅳ )，he wroted：symplectic geometry pervades a large part of the modern theory of linear partial differential operators with variable coefficients.And he had devoted the entire chapter ⅩⅩⅠto discuss it.