A slightly different motivation for fourier integral operators and pseudo-differential operators is given in the first chapter of this [book][1] - Fourier Integral Operators, chapter V. W. Guillemin: *[25 Years of Fourier Integral Operators](http://dx.doi.org/10.1007/978-3-662-03030-1_1)*. In this chapter, V. Guillemin presents this subject from the conormal bundles point of view and then shows how pseudo-differential operators are a special case of operators coming out of the Fourier distributions. 

Section 3 of this chapter also provides a historic outline of this theory. 

Interesting, Guillemin also shows here that pseudo-differential operators can be used to fine tune the theory of conormal distributions themselves -- giving a natural but unexpected application of pseudo-differential operators. 




  [1]: http://books.google.com/books?id=Zi1UzHg64xsC&pg=PA1