This thesis consists of four studies investigating various aspects relating to the microstructure of competitive dealership markets. Underlying the empirical work is detailed transaction and market maker quotation data obtained from the London Stock Exchange for a sample of thirty actively traded U.K. stocks over a one year period beginning in July 1991. The initial focus is on the characterization of the time series behaviour of market maker inventories. The null hypothesis of non-stationarity of inventories cannot uniformly be rejected for all market makers, and some explanations for this result are explored. Estimates of mean reversion coefficients of inventories are found to vary substantially in cross-section, and several determinants of this variation are identified. Some of the findings can be interpreted as evidence of subtle stock market linkages. This is followed by tests of a number of implications derived from the inventory control hypothesis specific to markets with competing dealers and inter-dealer trading (Ho and Stoll (1983)). Many of these implications relate to a dealer's inventory and quote position in relation to her competitors, and the results provide strong evidence that inventories are important in determining the trading outcome in a competitive dealership market. In the third study, the relationships among various spread-based measures of execution costs and dealer gross trading revenues are investigated. Revenues fall far short of the spread, implying that market maker spread gains are largely eroded by losses on the inventory positions. Spread measures are found to be highly correlated, suggesting that easily observable measures can serve as proxies for others. The fourth study is concerned with price setting in a competitive dealership market and addresses the question whether dealers set prices which reflect all their information or whether they act strategically by actively acquiring and subsequently exploiting informational advantages. The evidence supports the latter view.