This book is aimed at advanced undergraduates and it is intended as a primer in Harmonic Analysis. It is written without too much technical overload, opting to base the subject on the Riemann integral rather than the more demanding Lebesgue integral. This book has 3 goals. The first is to introduce the reader to Fourier analysis. The second is to explain how the Fourier series and the Fourier Transform are both special cases of a more general theory arising in the context of locally compact abelian groups. The third aim is to introduce the reader to the techniques used in Harmonic Analysis of noncommutative groups.

This book introduces harmonic analysis at an undergraduate level. In doing so it covers Fourier analysis and paves the way for Poisson Summation Formula. Another central feature is that is makes the reader aware of the fact that both principal incarnations of Fourier theory, the Fourier series and the Fourier transform, are special cases of a more general theory arising in the context of locally compact abelian groups. The final goal of this book is to introduce the reader to the techniques used in harmonic analysis of noncommutative groups. These techniques are explained in the context of matrix groups as a principal example.

* Fourier Series * Hilbert Spaces * The Fourier Transform * Finite Abelian Groups * LCA-groups * The Dual Group * The Plancheral Theorem * Matrix Groups * The Representations of SU(2) * The Peter-Weyl Theorem * The Riemann zeta function * Haar integration *