As well as a handful of corrections, this third edition includes various tweaks and changes aimed at making the material yet more accessible to the general reader. Two amendments stand out. Since first writing my book, I’ve struggled with the best way of explaining vectors and one-forms, the subject matter of the first half of chapter five. Different textbooks take different approaches, most of which IMHO are hard going for the non-specialist. I’ve now rewritten this section with the emphasis on vectors as infinitesimal displacements. Even I can sort of visualise giving a point on the manifold a tiny little nudge, and I’ve even included a diagram to make things clearer. I’ve also expanded the section on Schwarzschild geodesics in chapter nine, giving a full derivation of the radial motion equation. I’ve borrowed a couple of neat Taylor series approximations from Moore’s *A General Relativity Workbook* that allows the enthusiastic reader to model Schwarzschild orbits using just a spreadsheet. They work! Even using my old Excel 2000, I can generate the pretty flower-petal effect of a precessing orbit. The book is globally available as a paperback (ISBN 9780957389465) from Amazon and other retailers, as well as in Kindle and ePub format. Thanks to all those readers who took the trouble to give feedback and report errors.

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