Money Supply & Inflation?

Yes, obviously it does. Because if money is plentiful and easy to get, you get more people using it to buy stuff, thus higher demand, and since supply can't necessarily expand to meet demand then therefore higher prices.

The flip side of the coin is a tight money supply. Prices fall, but again it doesn't matter because in that case nobody has any money to buy stuff anyway.

Competing economic theories tend to concentrate on one or the side of this conundrum. The real focus should be on the ratio between them. The strength of the floating currency scheme for example is that it allows the money supply to be arbitrarily tweaked in this regard.