Elias M. Stein & Guido Weiss 
Introduction to Fourier Analysis on Euclidean Spaces [PDF ebook] 

The authors present a unified treatment of basic topics that arise in Fourier analysis. Their intention is to illustrate the role played by the structure of Euclidean spaces, particularly the action of translations, dilatations, and rotations, and to motivate the study of harmonic analysis on more general spaces having an analogous structure, e.g., symmetric spaces.