Banking in the modern sense of the word can be traced to medieval and early Renaissance Italy, to the rich cities in the north like Florence, Venice and Genoa. The Bardi and Peruzzi families dominated banking in 14th century Florence, establishing branches in many other parts of Europe. Perhaps the most famous Italian bank was the Medici bank, set up by Giovanni Medici in 1397. The earliest known state deposit bank, Banco di San Giorgio (Bank of St. George), was founded in 1407 at Genoa, Italy.
Banks can be traced back to ancient times even before money when temples were used to store commodities. During the 3rd century AD, banks in Persia and other territories in the Persian Sassanid Empire issued letters of credit known as Ṣakks. Muslim traders are known to have used the cheque or ṣakk system since the time of Harun al-Rashid (9th century) of the Abbasid Caliphate. In the 9th century, a Muslim businessman could cash an early form of the cheque in China drawn on sources in Baghdad, a tradition that was significantly strengthened in the 13th and 14th centuries, during the Mongol Empire. Fragments found in the Cairo Geniza indicate that in the 12th century cheques remarkably similar to our own were in use, only smaller to save costs on the paper. They contain a sum to be paid and then the order "May so and so pay the bearer such and such an amount". The date and name of the issuer are also apparent.
If you mean the formal setting up of a currency medium then Africa is probably the area to focus on. Africans were using anything another person would recognise as having value, to buy and trade, (this included other people). Obviously, they're a little bulky to carry around so currencies using shells and such developed, ( I have wondered why someone didn't just go to the beach and pick up some for free). Backed up by verbal promises, which allowed for flexibility, you had currency and credit. With a whole country maintaining that 3 cowrie shells = 2 glass beads you essentially had a bank.
The Medici family started the first banks in the Renaissance era. Today, the Medici Bank still exists in some areas.
Some argue the Knights Templar were the 1st bankers, holding travelers things while they were in the holy land, using a system of bank notes.
