A new translation of Euclid's 'Elements' together with a comprehensive introduction to each of the 'Elements'' books, all contained in a single volume. Euclid's 'Elements', produced c300 BC, superseded all previous attempts to identify the 'elements' of geometry and became the authoritative work on plane and solid geometry, number theory, proportion, and the irrationals to be relied upon and quoted by later Greek mathematicians. This edition contains a translation of Euclid's 'Elements' and discusses Euclid's methods - the development of axioms (postulates and common notions), the establishment of proofs derived from definitions, axioms and previously made proofs and the use of proof by contradiction. Each of the 'Elements' thirteen books is summarised and discussed in an introductory chapter. There is a fresh look at Euclid's treatment of rationality and commensurability, based as it was on comparisons of straight lines rather than numbers.