This thesis describes an inventory-theoretic approach to the study of the demand for money. It aims to connect money demand theory with optimal inventory theory on the one hand and with time series empirical evidence on the other. Thus it incorporates recent advances in inventory theory and extends these to allow the interest rate to follow a stochastic process. The problem of minimising the expected, discounted suns of cash-management costs is ascribed to an agent. Through the use of continuous-time, stochastic, optimal control an optimal cash-management policy is shown to exist and be of a familiar target-threshold form. Closed-form expressions for the forward-looking time-varying targets and thresholds are derived in special cases. The steady-state, Baumol-Tabin model, a further special case, also is examined in detail. The theory implies that expected future interest rates may influence money holdings despite the absence of strictly convex adjustment costs. A distributed-1ag expression for these holdings is proposed in which the adjustment and expectations dynamics are derived front theory. Aggregation over time and, to a lesser extent, over agents is treated explicitly. The econometric issues involved in testing models of the demand for money with rational expectations are outlined and simulation evidence on the predictions of the theory is provided. The theory gives rise to new predictions concerning expectations effects and variable adjustment speeds. It can also account for the findings of empirical research. In particular, it largely resolves the problem of slow adjustment in empirical money demand equations.