did they have societies?
The society was hierarchical with a sharp difference between the elite and the commoners.
Maya civilization
From the Early Preclassic, Maya society was sharply divided between the elite and commoners. As population increased over time, various sectors of society became increasingly specialised, and political organization became increasingly complex. 
how far back can we trace the mayan culture As far as circa 2000 BC what period of history is that? The Archaic period where were they located? The civilization encompassed areas of south-eastern Mexico, all of Guatemala and Belize, and the western portions of Honduras and El Salvador. did they practice politics? Yes, there were states and chiefdoms which had fluctuating policies towards one another.
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Maya civilization [SEP] Society
From the Early Preclassic, Maya society was sharply divided between the elite and commoners. As population increased over time, various sectors of society became increasingly specialised, and political organization became increasingly complex. By the Late Classic, when populations had grown enormously and hundreds of cities were connected in a complex web of political hierarchies, the wealthy segment of society multiplied. A middle class may have developed that included artisans, low ranking priests and officials, merchants, and soldiers. Commoners included farmers, servants, labourers, and slaves. According to indigenous histories, land was held communally by noble houses or clans. Such clans held that the land was the property of the clan ancestors, and such ties between the land and the ancestors were reinforced by the burial of the dead within residential compounds.