Final answer:
Peter the Great fought against the Swedish king Charles XII during the Great Northern War, with their most significant battle being the Battle of Poltava in 1709.
Step-by-step explanation:
The king of Sweden that Peter the Great fought was Charles XII. Peter the Great was the Tsar of Russia, and his military campaigns against Sweden were a part of the Great Northern War (1700-1721). During this conflict, he faced the young Swedish king, Charles XII, who was a formidable military leader. The most significant battle between Russia and Sweden during this period was the Battle of Poltava in 1709, where the Russian forces defeated the Swedish army, marking a turning point in the war that led to the decline of Swedish power in Europe and the rise of the Russian Empire.