If you are interested in Fractional Reserve Banking, then I suggest that you go read Zippy. He has more interesting, insightful and knowledgeable things to say then I will after another decade of study.
As a summary, fractional reserve banking does not increase the supply of money. [Update below] Money deposited at a bank is a sort of investment in the bank’s operation with an appropriate return on that investment based on your claim against the bank’s balance sheet. Your deposit followed by the bank’s operation of investing doesn’t create money anymore than buying stock creates money, its just that stock and bank deposits are different kinds of claims against some property with consequent rights associated with them.
Given this, what economists mean by the “money supply” is not the “supply of money.” The money supply then bundles together under the name “money” several different essentially different sorts of things. It would be worthwhile to understand what the “money supply” then means and how this interpretation affects theories and consequent conclusions based on it. But I haven’t worked that out yet.
Zippy also states this has to do with the presumption of usury in distorting the meaning of property and property claims. I don’t quite see all the pieces fitting together yet, but there’s a lot I don’t understand.
It does not seem that Zippy contends that the money supply does not increase. At the time of this writing, I was thinking of money as currency. Currency seems to be money primarily, but other assets are used as money in a secondary way. I think that what Zippy is getting at is that modern economics frequently fails to make good distinctions with respect to various kinds of contracts, assets and property. Fiat currency is a essentially different thing from a bank deposit denominated in fiat currency.