This book is intended for graduate students and advanced undergraduates, and mathematicians of whatever background who want a clear and concise overview of the subject of commutative harmonic analysis.
0. An overview of measure theory and functional analysis; 1. Fourier series basics; 2. The Fourier transform; 3. Multiple Fourier series; 4. Spherical harmonics; 5. Fractional integrals, singular integrals and Hardy spaces; 6. Modern theories of integral operators; 7. Wavelets; 8. A retrospective; Appendices.