Fourier Analysis

• The Fourier transform
• The inversion theorem, Plancherel's theorem

Sources

• Katznelson, Yitzhak (2004). An Introduction to Harmonic Analysis. Cambridge University Press. 
• Tao, Terence (2010). An Epsilon of Room, I. American Mathematical Society. http://bookstore.ams.org/gsm-117/14.