The Antikythera Mechanism, that dates from the first century B.C., is the only elaborate mechanical instrument to survive from antiquity. Unique and fragmentary as it is, it has, however, provided us with incontrovertible evidence that such devices existed in Hellenistic times. It became widely known through the work of Professor D.J. de S. Price, whose definitive paper was published in 1974. Several later scholars have presented variants of Price’s reconstruction; none of them, however, based his work on new research, and more has addressed the central problem, that Price’s observations are flawed and that many of his deductions may be challenged. The author has made anew, detailed investigation of the original fragments, which has led him to propose a radically different reconstruction of the Mechanism. According to this, the principal display was probably a planetarium, a type of instrument which, as literary evidence shows, was well known at that time. The author has made a working model of his reconstruction, to demonstrate that it is practicable. It has become clear that the original instrument is even less complete than earlier scholars have supposed, and so it is to be expected that problems will remain. Nevertheless, the author is continuing to analyze his data, with the intention of presenting as full an understanding of this instrument as possible.