The Raisonnier­Shelah construction of a non­measurable set Brian Semmes In this paper 1 we will give a proof of the following theorem of S. Shelah. Theorem 1: In Zermelo Fraenkel set theory (ZF) plus the axiom of dependent choice (DC), we can prove that there is a non­measurable set if there is an uncountable well­ordered set of reals. Shelah's proof uses rather sophisticated meta­mathematical arguments that may not be accessible to the general mathematician. As our principle goal is to reach a relatively wide audience, we will use the ideas of J. Raisonnier, who has given a simpler and less meta­mathematical proof of Theorem 1. However we will not follow Raisonnier's proof exactly. We will make some simplifications to Raisonnier's arguments and we will also follow to a certain extent the exposition of Raisonnier's proof presented in M. Bekkali's lecture notes for a seminar taught by S. Todorcevic.