A grad student in Italy just asked me to suggest topics for research in Money and Banking. Here is my reply:
I think the most important topic in Money and Banking in our time is how to replace fiat currencies and central banks with some kind of base money that cannot be debased or manipulated politically. Money should be independent of the political process. Banks should be allowed to issue their own currencies redeemable in that base money. Another way to put it is how to get money back under the “control” of distributed market processes and out of the control of central planners of any kind. Given the failure of central planning in so many ways, it is sad that we still have central planning of money, the most important single good in the economy.
Good luck with your studies,