Johan Palmstruch issued the first European banknotes starting in 1661. No 1661 dated examples are known to have survived but a 1662 example is shown above.

For another early European issue see the Norway - Jorgen Thør Mǿhlen notes which were issued in 1695.

The world's first banknotes issued were during the Tang Dynasty in China, ca. 618 - 907AD.  They were issued as certificates in various amounts and were transferable, therefore could be classified as paper money by our current definition.  These notes were referred to as flying money.