In this essay I define money to be whatever objects serve as generally acceptable media of exchange and I define monetary economics to be the study of the causes and economic consequences of the monetization of exchange -- that is, of the use of media of exchange. These definitions lead me to specify the distinctive objectives of monetary economics to be to understand (1) the monetization of exchange and its relation to the technologies of production and of exchange, (2) the form that money takes and, especially, the viability of fiat money, (3) the determination and significance of the real value of units of money, and (4) the relation between the nominal quantity of money and aggregate economic activity. The essay tries to acquaint the reader with the contents of the recently published "Handbook of Monetary Economic" as they relate to these objectives of monetary economics and offer some critical thoughts on selected unsettled issues in monetary economics that my reading of the "Handbook" suggested.
Grossman, H. I. (1991). Monetary economics. A review essay. Journal of Monetary Economics, 28(2), 323–345. https://doi.org/10.1016/0304-3932(91)90056-T