Two friendly proofs of the Berry-Esseen theorem

A gem of classical probability, the Berry-Esseen theorem provides a non-asymptotic form of the central limit theorem. This note gives a friendly and intuitive exposition of two different proofs of the Berry-Esseen theorem for nonidentically distributed random variables: the classical Fourier-analytic proof and a proof by Stein's method following E. Bolthausen. Both proofs are self-contained; the reader may read either proof without reading the other. The exposition is suitable for a basic graduate course in probability.