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This article accompanies a tutorial talk given at the 40th ACM STOC conference. In it, we give a brief introduction to Fourier analysis of boolean functions and then discuss some applications: Arrow's Theorem and other ideas from the theory of Social Choice; the Bonami-Beckner Inequality as an extension of Chernoff/Hoeffding bounds to higher-degree polynomials; and, hardness for approximation algorithms.doi:10.1145/1374376.1374458 dblp:conf/stoc/ODonnell08 fatcat:xhmjfdb5czbs5kew5obgpkxpnm