The following notes were prepared as the text of a set of lectures given at the Workshop in Geometry and Analysis, held at the Australian National University in January 1995, and aimed at a mixed audience of postgraduate students and academics.
The aim of the lecture series was ambitious: in five hours to start from the level of undergraduate Fourier analysis and bring the participants to the point where they could take subsequent advanced lecture courses on Calder6n-Zygmund theory, semigroup theory, distributions etc.
I have sought to give an overview of what I see as the important parts of the theory. There are no proofs or examples to speak of, indications of some of these being provided in lectures. An exception is in Chapter 5, where I felt that the proof of Malgrange-Ehrenpreis nicely drew together the rest of the material.
The last chapter provides an introduction to noncommutative harmonic analysis.