This book is a great introduction to the theory of Fourier series. If, like me, you're starting from scratch with a healthy calc background, you'll have no trouble using this book for self-study. The exercises are not trivial, but they won't take an hour each (like Whittaker & Watson).
My one gripe is that, aside from trig systems, Fourier-Bessel systems, and one paragraph on Legendre polynomials, they fail to give any other examples of complete orthogonal systems. If you're looking for a general book on orthogonal functions, this is not it. It is, however, a perfect introduction to the Fourier theory.