Korean is actually the national and official language of both South Korea, where it's called hangugeo, and North Korea, where it's known as chosonmal. In a few parts of China, it's a recognized minority language. Korean also has a presence in some regions of Central Asia and Russia. All in all, there are over 75 million people throughout the world who speak Korean.
While the language is mutually intelligible between North and South Korea, there are minor differences in several areas, notably in pronunciation, grammar, spelling, and vocabulary. Hangul is the Korean alphabet, which was introduced in the 13th century.