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The motivation for the study of Fourier integral operator can be illustrated by considering the following initial value problem for the wave operator: $$\partial^2 u(t,x) / \partial t^2 = \nabla^2 u(t,x)$$ where $(t,x)\in \mathbb{R}^+ \times \mathbb{R}^n$ and $u(0,x) = 0, \partial u(0,x) \partial t = f(x)$ where $f\in \mathcal{S}(\mathbb{R}^n)$.