Contemporaneous banking theory appear to understand financial institutions as intermediaries, neglecting some facts featuring modern banking: monetary financial institutions issue claims which function as money; they facilitate payments across agents in the economy over time and space; they increase the money base through credit creation; they hold fractional reserves and lend to each other. Our systemic perspective points to these featuring dimensions of ongoing bank activity. Our model considers bank activity process within each bank entity and across entities. Each bank keeps currency money in bank deposits on behalf of other agents. But the bank activity is further characterised by the capacity or privilege to use these deposits, although the latter remain available for payment and redemption at will and at par. Moreover, the bank can create deposit by granting a loan to, or buy a security from a borrower. This bank capacity or privilege involves money generation that enables the bank credit manufacturing process. In this way, all the banks become interdependent on the flow of payments that are performed across them, generating a ‘banking system’. Since each bank is structurally unbalanced due to money generation, inter-bank coordination is required to maintain the banking system in operation over time and circumstances. Both inter-bank clearing and credit arrangements provide this coordination at the inter-bank level, which is effectuated through central bank intervention, clearing houses and the money market. Institutional economic analysis and implications are developed for shadow banking; systemic risk, interdependency and interconnectedness; the relationship between money and credit and the real economy; and the systemic consistency between functions and institutions in monetary regimes.