Was there much of a formal banking system in medieval Europe, Arabia, or Asia? How did these systems develop? How did lending money and transactions go?
The question covers an astonishingly diverse time period and area. Narrowing the focus will produce better answers.
Let me be specific: how did banking begin in pre-Rennaisance Florence and how did the Medici family get over the historical stigma against moneylenders for them to have gained so much power?