Short answers, pulled from the story.
Greek colonists arrived along the southern coast of the Black Sea around 1000 BC. They named this region Pontus, derived from the Greek word for sea.
Mithridates I Ktistes created the Kingdom of Pontus shortly after 302 BC during the unsettled period following Alexander the Great's death. His descendant Mithridates VI Eupator led wars against Rome for many years under his rule.
Nero constituted the country as a Roman province in AD 62. It was divided into three districts: Pontus Galaticus, Pontus Polemoniacus, and Pontus Cappadocicus.
The Komnenos dynasty ruled this political entity for over two centuries. This remnant survived until conquered by Ottomans in 1461 following the Fall of Constantinople itself.
The Republic of Pontus was proposed at the Paris Peace Conference of 1919 but never came into existence. The Greek government of Eleftherios Venizelos feared its precarious position so it was included in Wilsonian Armenia instead.