Market making is central to the study of market microstructure. Market makers stand ready to provide liquidity, market stability and price discovery, issues of great importance to regulators, practitioners and academics. This thesis contributes to the literature by studying four topical issues related to market making. The thesis consists of four essays. In the first essay we develop a simple multi-period model of market making for a monopolistic stock market maker. The market maker tries to solve simultaneously the problems of managing his inventory and trading with informed traders. He uses a Kalman filter to update his estimates of the unknown market prices through his noisy order flow observation. We analytically characterize the optimal bid and ask prices and find that they depend on the beginning inventory, the estimated price, and the market maker's prior estimation error of the price process for each time period. We obtain desirable numerical results by using properly chosen parameters. The extensions to the continuous time and a competitive market making environment are also discussed. The second essay extends the model in the first essay to consider the market making of multiple stocks. The market maker still does not know the true prices but is assumed to know the return covariance structure of these stocks. When the market maker considers the correlated order flow information, his knowledge of the return covariance improves his estimation of the unknown price processes, resulting in higher cumulative profits and lower risks of the profits. The third essay analyzes the effect of option market makers' hedging on the informed trading strategy and the subsequent changes in the costs of liquidity provision in both stock and option markets. In a sequential trading framework, an option market maker uses the stock market to hedge his option position. His hedging trade affects the way that informed traders submit their orders in both the stock and the option market, which in turn changes the informed trading pressure faced by the market makers in each market. Furthermore, information in the option trading is passed to the stock market through the hedging trade. Both stock and option spreads are wider with option market maker's hedging. The increase in the spreads is more significant when the option market maker hedges in the underlying market than when it hedges with different options. The fourth essay provides a model of bookmaking in a horse race betting market. The bookmaker observes the noisy public betting flow and faces the risk of trading with possible informed traders, as well as the risk of his unbalanced liability exposures. Even the noisy demand can unbalance the bookmaker's book. In our model, the bookmaker revises his odds to mitigate the risk. Allowing the bookmaker to set odds over several rounds of betting gives a clear view of the bookmaker's price setting strategy and its impact on the public betting flow over time. The study of horse race bookmaking provides useful insights into the market making of state contingent claims such as options.