It is the first calculating machine in history. It was used to determine and forecast important astronomical and calendar events. Its remains were found accidentally by sponge divers in 1900 in the eminent shipwreck off the island of Antikythera. Its manufacture dates from around 120 B.C. and it is probably the product of a Rhodian or an Asia Minor workshop, which developed the tradition of Archimedes’ “Sphere-Making”, with its direct inspirators being Hipparchus or Posidonius. It consisted of indicators, scales and at least thirtyfive cooperating gear wheels that were moved by a handle. At the front it had a circular scale of the 365 days with the possibility of adding one additional day every four years. At the back it had the spiral scales of the Metonic and Saros cycles and also the Callippic cycle, the “Exeligmos” cycle and the Athletic Games cycle (Olympiad). With the rotation of the handle, and consequently the choice of a date on the front scale of 365 days, the remainder indicators give us all available astronomical information thereon (e.g. position and phase of the moon, matching of solar-lunar calendar, etc.). Reversely, if the operator of the mechanism brings the indicator to some particular astronomical or calendar events, (e.g. an eclipse of the moon or a performance of the Olympic Games) he can see the date (even the hour) that this will happen in the future or happened in the past. Solla De Price and Michael Wright were the most important researchers of this mechanism. This reconstruction reflects the constructional opinion of the author that was based on the new data from the International Study Team of the Antikythera Mechanism.