Theon of Smyrna, a neo-Platonic commentator of the third century ad, wrote a book Expositio Rerum Mathematicarum ad Legendum Platonem Utilium', with a little less hubris than Theon, I regard this book here as 'An Account of Mathematical Topics that May be Useful for Reading Some Bits of Plato'. But, at the outset, I must emphasise that, like Theon, I do not deal with Plato's philosophy. My objective is to provide a background, developed around a new interpretation of aspects of early Greek mathematics, against which to set some of our evidence about the activities of Plato and his colleagues in the Academy. The exposition is divided into three parts, each with its own introduction; the following brief preface, together with these introductions, will give a summary of the aims, contents, and organisation of the book.