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In the territory of today's Mexico, Guatemala, Belize, northwestern El Salvador, and western Honduras, important Native American cultures were formed over the course of millennia. Among them, the Mayan culture stands out in particular. Its development from simple villages to magnificent temple cities took place similarly to other Indian cultures of Mexico. However, they differ from them mainly in the field of spiritual culture, in which the Maya reached a level that surpassed their simple technological possibilities. The Maya created a system of hieroglyphic writing and a complex calendar. The results of their astronomical observations, or calculations, related to tracking the course of the tropical year, determining the lengths of the synodic orbits of all visible planets, determining the times of their mutual positions and conjunctions, maximum elongations of Mercury and solar eclipses are also excellent. The lecture will be dedicated to the Mayan calendar system, the derivation of the relationship between the Mayan and our dating, and mainly the Mayan records of astronomical observations, which we have used for this purpose over the past decades. We used the Dresden Codex, one of only four surviving Maya written monuments, as a source for this information. It currently contains an unexpectedly large number of these records, and we keep discovering new ones in it. The lecture is dedicated to the late Ing. To Bohumil Bőhm, who was at the origin of these studies from the very beginning and from whose preserved notes we still draw. The lecture is organized by the Jihlava Vysočina Museum in cooperation with the Jihlava Astronomical Society and the Vysočina Branch of the Czech Astronomical Society. In case of any questions or comments, write to [email protected] Presented in Jihlava on 14 September 2023