The Fourier expansion of a boolean function $f : \{-1,1\}^n \to \{-1,1\}$ is simply its representation as a real, multilinear polynomial. (Multilinear means that no variable $x_i$ appears squared, cubed, etc.) For example, suppose $n = 2$ and $f = {\textstyle \min_2}$, the “minimum” function on $2$ bits:

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Ryan O'Donnell: Thanks! It's corrected in the book.Ohad Klein: In theorem 44, I think the written taylor expansion is the o...Ryan O'Donnell: Yes, thanks!Noam Lifshitz: In exercise 15 (Ex 18 in the book) is it true that $V_j=T_j$...Ryan O'Donnell: Thanks!Matt Franklin: Maybe two small typos in the proof of Corollary 11.67 (p. 36...Ryan O'Donnell: I see your point, although in some sense this distinction be...