I was wondering whether to spruce up my very rapidly written hand-outs on Gödel's Theorems which I produced for the Cameleon weekend and publish them here. I was beginning to think I wouldn't bother, as there are other things I want to be getting on with. But I just now read the chapter on incompleteness in Shawn Hedman's A First Course in Logic, and that reminded me how crummy some textbook treatments can be, and hence of the need for crisp and clear presentations. Not that Hedman is technically wrong, of course (well, I haven't read him that carefully, but the details look ok). But I defy any beginning student to take away from his chapter a really clear sense of what the key big ideas are, or of how to distinguish the general results from the hack-work needed to show that they apply to this or that particular theory. So back to those hand-outs!