Classical Greece is the oldest I'm aware of, though it could have been developed beforehand. Herodotus (d. 425 BCE) wrote "Histories" (http://classics.mit.edu/Herodotus/history.html), which I believe is the first known work to truly be considered as part of the study of history, involving research considering multiple viewpoints (an notably assessing their reliability) as well as travels to different locations in order to get different perpectives. That works focused mostly on Mediterranian cultures, including notably the clashes between the Greek city-states and the Persian Empire.

Before that I believe it was mostly chroniclers preserving what was taking place, or individuals putting the oral tradition into written language.

China had written historical accounts dating back several hundred years before, but they were more chronicles than true studies of history.