Abstract. In this review the oldest known advanced astronomical instrument and dedicated analogue computer is presented, in context. The Antikythera Mechanism a mysterious device, assumed to be ahead of its time, probably made around 150 to 100 BCE, has been found in a 1st century BCE shipwreck near the island of Antikythera in a huge ship full of Greek treasures that were on their way to Rome. The Antikythera Mechanism is a clock-like device made of bronze gears, which looks much more advanced than its contemporary technological achievements. It is based on mathematics attributed to the Hipparchus and possibly carries knowledge and tradition that goes back to Archimedes, who according to ancient texts constructed several automata, including astronomical devices, a mechanical planetarium and a celestial sphere. The Antikythera Mechanism probably had a beautiful and expensive box; looking possibly like a very elaborate miniature Greek Temple, perhaps decorated with golden ornaments, of an elegant Hellenistic style, even perhaps with automatic statuettes, 'daemons', functioning as pointers that performed some of its operations. Made out of appropriately tailored trains of gears that enable to perform specialised calculations, the mechanism carries concentric scales and pointers, in one side showing the position of the Sun in the ecliptic and the sky, possibly giving the time, hour of the day or night, like a clock. The position of the Moon and its phase is also shown during the month. On the other side of the Mechanism, having probably the size of a box (main part 32×20×6 cm), are two large spiral scales with two pointers showing the time in two different very long calendars, the first one concerning the eclipses, and lasting 18 years 11 days and 8 hours, the Saros period, repeating the solar and lunar eclipses, and enabling their prediction, and the 19 year cycle of Meton, that is the period the Moon reappears in the same place of the sky, with the same phase. An additional four-year dial shows the year of all Greek Festivities, the so-called 'games' (Olympic, Pythian, Isthmian etc). Two additional dials give the Exeligmos, the 54 year and 34 day cycle, which provides a more accurate prediction of eclipses. It is possible that the Mechanism was also equipped with a planetary show display, as three of the planets and their motion (stationary points) are mentioned many times in the manual of the instrument, so it was also a planetarium. From the manual we have hints that the mechanism was probably also an observational instrument, as having instructions concerning a viewfinder and possibly how to orient the viewfinder to pass a sunbeam through it, probably measuring the altitude of the Sun. There are fragmented sentences that probably give instructions on how to move the pointers to set the position of the Sun, the Moon and the planets in their initial places in the ecliptic, on a specific day, or how to measure angular distances between two celestial bodies or their coordinates. This mechanism is definitely not th...