One of the main problems in the the study of Parmenides’ poem is establishing the meaning of e‰nai, ‘to be’. Scholars often simply take it to mean: ‘to exist’, ‘to be the case’, ‘to be so’, or regard it as a copula. It’s better to start by fathoming what Parmenides himself has to say about to be and about Being. This cannot be done without recognizing the logical pattern in his poem. Another main problem is: what does not-Being mean? Is the so-called Doxa - as not-Being - a non-existing, hallucinatory world, an illusion, a fata morgana? Or is it only a detector of lies? In the present work the view will be advocated that the Doxa offers the description of a really existing world. A specific merit of this book is that all the problems involved will be examined in continuous debate with what scholars have offered as solutions so far.