# Introduction to Pseudodifferential operators

I'm interested in elementary introduction to pseduodifferential operators and its application to hyperbolic PDE's. I know measure theory, Fourier analysis and some elementary(linear) hyperbolic PDE's but not functional analysis, distributions, Sobolev spaces,etc. Can you recommend suitable intro text? Thanks

There is of course Hörmander's magnum opus The Analysis of Linear Partial Differential Operators (Springer); pseudodifferential operators are discussed in volume III.

Less technical is Michael Taylor's book Pseudodifferential Operators (Princeton University Press). He also has a set of lecture notes and a pdf of his book Pseudodifferential Operators and Nonlinear PDEs (Birkhäuser) on his website.

The easiest introduction is "An Introduction to Pseudo-differential Operators by "M. W. Wong". However it is not so general as Hörmander or Taylor. It develops the theory only for the classes $S^m_{1, 0}$. The requisites are very modest. Another nice reading is "Pseudo-differential and Singular Integral Operators" by "H. Abels".

The best introduction is Raymond Elementary Introduction to the Theory of Pseudodifferential Operators CRC Press.